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Stochastik (Einführung in die Wahrscheinlichkeitstheorie) PDF-Datei (Neue Version von 2020, die allerdings einer weiteren Überarbeitung bedarf) Mathematische Statistik PDF-Datei Stochastische Prozesse PDF-Datei (Englisch) Martingale PDF-Datei Extremwerttheorie PDF-Datei (Version vom 17.07.2015) Aufgaben zur Stochastik, Teil 1 Aufgaben und Ergebnisse zur Selbstkontrolle Aufgaben zur Stochastik, Teil 2 Aufgaben und Ergebnisse zur Selbstkontrolle Aufgaben zur Stochastik, Teil 3 Aufgaben (Leider ohne Ergebnisse zur Selbstkontrolle) Aufgaben zur mathematischen Statistik Teil 1 und Teil 2 (Leider ohne Ergebnisse zur Selbstkontrolle) Aufgaben zur Stochastik für Lehrämtler Teil 1 und Teil 2, Ergebnisse 1 und Ergebnisse 2 Publications
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Preprints at arxiv.org: Link
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Jonas Jalowy, Zakhar Kabluchko, Matthias Löwe (2024)
Propagation of chaos and residual dependence in Gibbs measures on finite sets.
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Michael Juhos, Zakhar Kabluchko, Joscha Prochno (2024)
Asymptotic theory of Schatten classes.
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Alexander Iksanov, Zakhar Kabluchko, Alexander Marynych, Vitali Wachtel (2024)
Multinomial random combinatorial structures and r-versions of Stirling, Eulerian and Lah numbers.
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Gerold Alsmeyer, Alexander Iksanov, Zakhar Kabluchko (2024)
On decoupled standard random walks.
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Brian C. Hall, Ching-Wei Ho, Jonas Jalowy, Zakhar Kabluchko (2023)
Roots of polynomials under repeated differentiation and repeated applications of fractional differential operators.
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Matthias Löwe, Zakhar Kabluchko (2023)
Propagation of chaos in the Random field Curie-Weiss model.
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Zakhar Kabluchko and Alexander Marynych (2023)
Divisibility properties of polynomial expressions of random integers. J. Number Theory, Vol. 259, pages 357-377, 2024.
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Brian C. Hall, Ching-Wei Ho, Jonas Jalowy, Zakhar Kabluchko (2023)
Zeros of random polynomials undergoing the heat flow.
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Jonas Jalowy, Zakhar Kabluchko, Matthias Löwe, Alexander Marynych (2023)
When does the chaos in the Curie-Weiss model stop to propagate? Elect. J. Probab., 28 (2023), article no. 139, 1–17.
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Kabluchko, Z., Marynych, A., Raschel, K. (2023)
Random walks in the high-dimensional limit II: The crinkled subordinator. Stochj. Proc. Appl., Vol. 176, October 2024, 104428.
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Hall, B., Ho, C.-W., Jalowy, J., Kabluchko, Z. (2023)
The heat flow, GAF, and SL(2;R). Indiana Univ. Math. Journal, accepted.
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Kabluchko, Z., Rosen, D. and Thäle, C. (2023)
A quantitative central limit theorem for Poisson horospheres in high dimensions. Electron. Commun. Probab. 29: 1-11 (2024).
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Kabluchko, Z., Prochno, J., and Sonnleitner, M. (2023)
A probabilistic approach to Lorentz balls. J. of Funct. Analysis, Vol. 288(1), 110682.
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Kabluchko, Z. and Marynych, O. and Raschel, K. (2023)
Multivariate multiplicative functions of uniform random vectors in large integer domains. Results in Math., 78, Article number: 201, 2023.
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Gusakova, A., Kabluchko, Z., Thäle. C. (2023)
Sectional Voronoi tessellations: Characterization and high-dimensional limits. Bernoulli, 30(2): 1482-1501, 2024.
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Kabluchko, Z., Steigenberger, D. A. (2022)
r-Lah distribution: properties, limit theorems and an application to compressed sensing. Adv. in Appl. Math., Vol. 150, 2023, 102575.
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Iksanov, A., Kabluchko, Z., Kotelnikova, V. (2022)
A law of the iterated logarithm for iterated random walks, with application to random recursive trees.
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Kabluchko, Z., and Marynych, A. (2022)
Random Walks in the High-Dimensional Limit, I. Ann. Inst. H. Poincare, accepted.
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Juhos, M., Kabluchko, Z., Prochno, J. (2022)
Limit theorems for mixed-norm sequence spaces with applications to volume distribution. Electron. J. Probab. 29: 1-44 (2024).
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Kabluchko, Z., Marynych, A., Pitters, H. (2022)
Mod-$\varphi$ convergence of Stirling distributions and limit theorems for zeros of their generating functions. J. Math. Anal. Appl., Vol. 529(1), 2024, 127571.
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Kabluchko, Z., Rosen, D,. Thäle, C. (2022)
Fluctuations of λ-geodesic Poisson hyperplanes in hyperbolic space. Israel J. Math., accepted.
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Kabluchko, Z. (2022)
Lee-Yang zeroes of the Curie-Weiss ferromagnet, unitary Hermite polynomials, and the backward heat flow.
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Kabluchko, Z., Marynych, A., Molchanov, I. (2022)
Generalised convexity with respect to families of affine maps. Israel J. Math., accepted.
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Kabluchko, Z. (2021)
Repeated differentiation and free unitary Poisson process.
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Kabluchko, Z. and Prochno, J. (2021)
Large deviations for random matrices in the orthogonal group and Stiefel manifold with applications to random projections of product distributions. Ann. Inst. H. Poincare, 60(2): 990-1024.
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Kabluchko, Z. (2021)
Face numbers of high-dimensional Poisson zero cells. Proc. AMS, 151, pp. 401-415, 2023.
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Godland, T., Kabluchko, Z., Thäle, C. (2021)
Beta-star polytopes and hyperbolic stochastic geometry. Advances in Math., Vol. 404(A), 108382, 2022.
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Gusakova, A., Kabluchko, Z., Thäle, C. (2021)
The $\beta$-Delaunay tessellation IV: Mixing properties and central limit theorems. Stochastics and Dynamics, Vol. 23, No. 03, 2350021 (2023).
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Kabluchko, Z. (2021)
On expected face numbers of random beta and beta' polytopes. Contrib. Alg. and Geom., 64: 155–174, 2023.
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Godland, T., Kabluchko, Z., Thäle, C. (2021)
Random cones in high dimensions II: Weyl cones. Mathematika, 68(3), pp. 710-737, 2022.
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Kabluchko, Z. and Marynych, A. (2021)
Lah distribution: Stirling numbers, records on compositions, and convex hulls of high-dimensional random walks. Probab. Theory and Rel. Fields, 184, pp. 969-1028, 2022.
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Gusakova, A., Kabluchko, Z., Thäle, C. (2021)
The $\beta$-Delaunay tessellation III: Kendall's problem and limit theorems in high dimensions. ALEA, 19(2022), 23-50.
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Iksanov, A., Kabluchko, Z., Kotelnikova, V. (2021)
A functional limit theorem for nested Karlin's occupancy scheme generated by discrete Weibull-like distributions. J. Math. Anal. Appl., Volume 507(2), 2022, 125798
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Godland, T. and Kabluchko, Z. (2021)
Positive hulls of random walks and bridges. Stoch. Proc. and Appl., Vol. 147, pp. 327-362, 2022.
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Johnston, S. G. G., Kabluchko, Z., Prochno, J. (2021)
Projections of the uniform distribution on the cube - a large deviation perspective. Studia Math., 264 (2022), 103-119.
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Gusakova, A., Kabluchko, Z., Thäle, C. (2021)
The β-Delaunay tessellation II: The Gaussian limit tessellation. Elect. J. Probab., 27: 1-33 (2022).
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Kabluchko, Z., Löwe, M,. Schubert, K. (2020)
Fluctuations of the magnetization for Ising models on Erdős-Rényi random graphs - the regimes of low temperature and external magnetic field. ALEA, 19(2022), 537-563.
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Godland, T., Kabluchko, Z., Thäle, C. (2020)
Random cones in high dimensions I: Donoho-Tanner and Cover-Efron cones. Discrete Analysis, 2020:5.
Preprint at arxiv.org: Link (This is the final version of the article)
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Aistleitner, C., Gantert, N., Kabluchko, Z., Prochno, J., Ramanan, K. (2020)
Large deviation principles for lacunary sums. Trans. Amer. Math. Soc., 376(1), pages 507–553, 2023.
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Hoskins, J., Kabluchko, Z. (2020)
Dynamics of zeroes under repeated differentiation. Experimental Math., Vol. 32(4), pp. 573-599, 2023.
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Godland, T., Kabluchko, Z. (2020)
Projections and angle sums of belt polytopes and permutohedra. Results in Math., 78, Article number 140, 2023.
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Kabluchko, Z. (2020)
An identity for the coefficients of characteristic polynomials of hyperplane arrangements. Discr. and Comput. Geometry, Vol. 70, p. 1476-1498, (2023).
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Kabluchko, Z. and Prochno, J. (2020)
The maximum entropy principle and volumetric properties of Orlicz balls. J. Math. Anal. Appl., Vol. 495(1), 124687, 2021.
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Godland, T., Kabluchko, Z., Zaporozhets, D. (2020)
Angle sums of random polytopes. Michigan Math. J., 73(4), pp. 815-842, 2023.
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Godland, T., Kabluchko, Z. (2020)
Angle sums of Schläfli orthoschemes. Discr. and Comput. Geometry, 68(1), pp. 125–164 (2022).
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Kabluchko, Z., Seidel, H. (2020)
Convex cones spanned by regular polytopes. Adv. in Geom., 22(2), pp. 245-267, 2022.
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Gusakova, A., Kabluchko, Z., and Thäle, C. (2020)
The β-Delaunay tessellation I: Description of the model and geometry of typical cells. Adv. Appl. Probab., 54(4), pp. 1252 - 1290, (2022).
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Godland, T. and Kabluchko, Z. (2020)
Conic intrinsic volumes of Weyl chambers. Modern Stochastics, Vol. 9(3), pp. 357–375, 2022.
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Baci, A., Kabluchko, Z., Prochno, J., Sonnleitner, M., Thäle, C. (2020)
Limit theorems for random points in a simplex. J. Appl. Probab., 59(3), pp. 685 - 701, 2022.
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Kabluchko, Z., Thäle, C. (2020)
Faces in random great hypersphere tessellations. Elect. J. Probab., Vol. 26 (2021), paper no. 3.
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Godland, T. and Kabluchko, Z. (2020)
Conical tessellations associated with Weyl chambers. Trans. Amer. Math. Soc., 374(10), pp. 7161–7196 (2021).
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Kabluchko, Z., Temesvari, D., Thäle, C. (2020)
A new approach to weak convergence of random cones and polytopes. Canad. J. Math., 73 (6), pp. 1627-1647, 2021.
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Kabluchko, Z., Löwe, M., Schubert, K. (2020)
Fluctuations for the partition function of Ising models on Erdös-Rényi random graphs. Ann. Inst. H. Poincare, 57(4): 2017-2042.
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Bonnet, G., Kabluchko, Z., Turchi, N. (2019)
Phase transition for the volume of high-dimensional random polytopes. Rand. Struct. Algor., Vol. 58(4), pp. 648-663, 2021.
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Kabluchko, Z., Löwe, M., Schubert, K. (2019)
Fluctuations of the magnetization for Ising models on Erdős-Rényi random graphs - the regimes of small $p$ and the critical temperature. J. Phys A. Math. Theor., Vol. 53, 355004.
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Kabluchko, Z., Thäle, C. (2019)
The typical cell of a Voronoi tessellation on the sphere. Discr. and Comput. Geometry, 66(2021), 1330-1350 .
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Götze, F., Kabluchko, Z., Zaporozhets, D. (2019)
Grassmann angles and absorption probabilities of Gaussian convex hulls. Zap. Nauchn. Sem. POMI, 501, pp. 126-148, 2021.
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Kabluchko, Z., Prochno, J., and Thäle, C. (2019)
A new look at random projections of the cube and general product measures. Bernoulli, 27(3), pp. 2117-2138, 2021.
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Kabluchko, Z. (2019)
Angles of random simplices and face numbers of random polytopes. Advances in Math., Vol. 380, 107612, 2021.
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Alsmeyer, G., Kabluchko, Z., Marynych, A., Vysotsky, V. (2019)
How long is the convex minorant of a one-dimensional random walk? Elect. J. Probab., Vol. 25 (2020), paper no. 105.
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Kabluchko, Z. (2019)
Recursive scheme for angles of random simplices, and applications to random polytopes. Discr. and Comp. Geometry, Vol. 66, 902-937 (2021).
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Kabluchko, Z., Löwe, M., Schubert, K. (2019)
Fluctuations of the magnetization for Ising models on dense Erdős-Rényi random graphs. J. Stat. Phys., 177(1), pp. 78–94, 2019.
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Kabluchko, Z. (2019)
Angle sums of random simplices in dimensions 3 and 4. Proc. Amer. Math. Soc., 148(7), pp. 3079–3086, 2020.
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Kabluchko, Z., Prochno, J., and Thäle, C. (2019)
High-dimensional limit theorems for random vectors in l_p^n-balls. II. Comm. in Contemp. Math., Vol. 23(03), 1950073 (2021).
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Alonso-Gutierrez, D., Besau, F., Grote, J., Kabluchko, Z., Reitzner, M., Thäle, C., Vritsiou, B.-H., Werner, E. (2019)
Asymptotic normality for random simplices and convex bodies in high dimensions. Proc. Amer. Math. Soc., 149 (2021), 355-367.
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Kabluchko, Z. and Wigman, I. (2019)
Asymptotics for the expected number of nodal components for random lemniscates. Internat. Math. Res. Notices, , Vol. 2022 (3), pp. 2337-2375.
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Kabluchko, Z. (2019)
Expected $f$-vector of the Poisson zero polytope and random convex hulls in the half-sphere. Mathematika, Vol. 66(4), pp. 1028-1053, 2020.
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Kabluchko, Z. (2018)
An infinite-dimensional helix invariant under spherical projections. Elect. Comm. Probab., 24, no. 25, 1-13, 2019.
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Kabluchko, Z., Zaporozhets, D. (2018)
Angles of the Gaussian simplex. Zap. Nauchn. Sem. POMI, 476, pp. 79-91, 2018.
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Götze, F., Gusakova, A., Kabluchko, Z., Zaporozhets, D. (2018)
Distribution of complex algebraic numbers on the unit circle. Zap. Nauchn. Sem. POMI, 474, pp. 90-107, 2018.
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Kabluchko, Z., Prochno, J., Vysotsky V. (2018)
Yet another note on the arithmetic-geometric mean inequality. Studia Math., 253, pp. 39-55, 2020.
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Kabluchko, Z., Prochno, J., and Thäle, C. (2018)
Sanov-type large deviations in Schatten classes. Ann. Inst. H. Poincare, Vol. 56(2), pp. 928-953, 2020.
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Kabluchko, Z., Seidel, H. (2018)
Distances between zeroes and critical points for random polynomials with i.i.d. zeroes. Elect. J. Probab., 24(2019), paper 34.
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Iksanov, A., Kabluchko, Z. (2018)
Weak convergence of the number of vertices at intermediate levels of random recursive trees. J. Appl. Probab., 55(4), pp. 1131-1142.
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Kabluchko, Z., Thäle, C., and Zaporozhets, D. (2018)
Beta polytopes and Poisson polyhedra: f-vectors and angles. Advances in Math., Vol. 374, 18 November 2020, 107333.
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Kabluchko, Z., Prochno, J., and Thäle, C. (2018)
Exact asymptotic volume and volume ratio of Schatten unit balls. J. Approx. Theory, Vol. 257, 105457, September 2020.
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Kabluchko, Z., Prochno, J., and Thäle, C. (2018)
Intersection of unit balls in classical matrix ensembles. Israel J. Math., 239, 129–172 (2020).
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Flasche, H., Kabluchko, Z. (2018)
Real zeros of random analytic functions associated with geometries of constant curvature. J. Theor. Probab., 33(1), 103-133, 2020.
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Alsmeyer, G., Kabluchko, Z., Marynych, A. (2018)
Limit theorems for the least common multiple of a random set of integers. Trans. Amer. Math. Soc., 372(7), pp. 4585–4603, 2019.
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Kabluchko, Z., Marynych, A., Temesvari, D., Thäle, C. (2018)
Cones generated by random points on half-spheres and convex hulls of Poisson point processes. Probab. Theory and Rel. Fields, 175, pp. 1021–1061, 2019.
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Iksanov, A., Kabluchko, Z. (2018)
A functional limit theorem for the profile of random recursive trees. Elect. Comm. Probab., 23(2018), no. 87, 1–13.
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Kabluchko, Z., Tent, K. (2017)
On weak Fraïssé limits.
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Kabluchko, Z., Tent, K. (2017)
Universal-homogeneous structures are generic.
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Kabluchko, Z., Prochno, J., and Thäle, C. (2017)
High-dimensional limit theorems for random vectors in l_p^n-balls. Comm. in Contemp. Math., Vol. 21, No. 01, 1750092 (2019).
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Flasche, H., Kabluchko, Z. (2017)
Expected number of real zeros of random Taylor series. Comm. in Contemp. Math., Vol. 22, No. 07, 1950059 (2020).
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Kabluchko, Z., Lifshits, M. (2017)
Adaptive energy saving approximation for stationary processes. Russian version: Izvestiya RAN (Ser. Mat.) 83(5), pp. 27–52, 2019. English version: Izvestiya Mathematics, 83(5), pp. 932–956, 2019.
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Grote, J., Kabluchko, Z., and Thäle, C. (2017)
Limit theorems for random simplices in high dimensions. ALEA, 16(2019), 141-177.
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Kabluchko, Z., Temesvari, D. and Thäle, C. (2017)
Expected intrinsic volumes and facet numbers of random beta-polytopes. Math. Nachr., 292(1), pp. 79-105, 2019.
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Mathematica notebooks: Beta-Polytopes Beta'-Polytopes -
Kabluchko, Z., Zaporozhets, D. (2017)
Expected volumes of Gaussian polytopes, external angles, and multiple order statistics. Trans. Amer. Math. Soc., 372(3), 1709-1733, 2019.
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Kabluchko, Z., Zaporozhets, D. (2017)
Absorption probabilities for Gaussian polytopes, and regular spherical simplices. Adv. Appl. Probab., Vol. 52(2), pp. 588-616, June 2020.
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Kabluchko, Z., Thäle, C. (2017)
Monotonicity of expected f-vectors for projections of regular polytopes. Proc. Amer. Math. Soc., 146(3), pp. 1295–1303, 2018.
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Hug, D., Kabluchko, Z. (2016)
An inclusion-exclusion identity for normal cones of polyhedral sets. Mathematika, 64 (2018), 124-136.
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Iksanov, A., Kabluchko, Z. (2016)
Functional limit theorems for Galton-Watson processes with very active immigration. Stoch. Proc. Appl., Volume 128(1), Pp. 291-305, 2018.
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Kabluchko, Z., Vysotsky, V., Zaporozhets, D. (2016)
Convex hulls of random walks: Expected number of faces and face probabilities. Advances in Math., Vol. 320(7), pp. 595-629, 2017.
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Ibragimov, I., Kabluchko, Z., Lifshits, M. (2016)
Some extensions of linear approximation and prediction problems for stationary processes. Stoch. Proc. Appl., Vol 129(8), pp. 2758-2782, 2019.
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Kabluchko, Z., Vysotsky, V., Zaporozhets, D. (2016)
A multidimensional analogue of the arcsine law for the number of positive terms in a random walk. Bernoulli, Vol. 25(1), pp. 521-548, 2019.
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Kabluchko, Z., Marynych, A., Sulzbach, H. (2016)
Mode and Edgeworth expansion for the Ewens distribution and the Stirling numbers. J. Integer Sequences, 19 (2016), Article 16.8.8.
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Mathematica notebook: Download the notebook The same as PDF
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Alsmeyer, G., Kabluchko, Z., Marynych, A. (2016)
Leader election using random walks. ALEA, 13(2016), 1095-1122.
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Kabluchko, Z., Marynych, A., Sulzbach, H. (2016)
General Edgeworth expansions with applications to profiles of random trees. Ann. Appl. Probab., 27(6), pp. 3478-3524, 2017.
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Kabluchko, Z., Marynych, A. (2016)
Renewal shot noise processes in the case of slowly varying tails. Theor. Stoch. Proc., Vol.21 (37), no.2, pp.14-21, 2016.
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Kabluchko, Z., Last, G., Zaporozhets, D. (2016)
Inclusion-exclusion principles for convex hulls and the Euler relation. Discr. and Comp. Geometry, 58(2), p. 417-434, 2017.
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Iksanov, A., Kabluchko, Z. Marynych, A. Shevchenko, G. (2016)
Fractionally integrated inverse stable subordinators. Stoch. Proc. Appl., 127(1), pp. 80-106, 2017.
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Iksanov, A., Kabluchko, Z., Marynych, A. (2016)
Local universality for real roots of random trigonometric polynomials. Elect. J. Probab., Vol. 21 (2016), paper no. 63.
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Dombry, C., Kabluchko, Z. (2016)
Ergodic decompositions of stationary max-stable processes in terms of their spectral functions. Stoch. Proc. Appl., 127(6), pp. 1763-1784, 2017.
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Alsmeyer, G., Kabluchko, Z., Marynych, A. (2015)
A leader-election procedure using records. Ann. Probab., 45(6B), pp. 4348-4388, 2017.
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Kabluchko, Z., Litvak, A. E., Zaporozhets, D. (2015)
Mean width of regular polytopes and expected maxima of correlated Gaussian variables. Zap. Nauchn. Sem. POMI, 442, pp. 75-96, 2015, and J. of Math. Sci., 225(5), pp. 770-787, 2017.
Preprint at arxiv.org: Link
Publisher's homepage (Zap. Nauchn. Sem. POMI): Link
Publisher's homepage (J. of Math. Sci.): Link -
Kabluchko, Z., Vysotsky, V., Zaporozhets, D. (2015)
Convex hulls of random walks, hyperplane arrangements, and Weyl chambers. Geom. Funct. Anal., 27(4), p. 880-918, 2017.
Preprint at arxiv.org: Link
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Engelke, S., Kabluchko, Z. (2015)
A characterization of the normal distribution using stationary max-stable processes. Extremes, 19(2016), pp 1-6.
Preprint at arxiv.org: Link
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Iksanov, A., Kabluchko, Z. (2015)
A central limit theorem and a law of the iterated logarithm for the Biggins martingale of the supercritical branching random walk. J. Appl. Probab., Volume 53(4), pp. 1178-1192, 2016.
Preprint at arxiv.org: Link
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Iksanov, A., Kabluchko, Z., Marynych, A. (2015)
Weak convergence of renewal shot noise processes in the case of slowly varying normalization. Statist. Probab. Letters, 114 (2016), pp. 67-77.
Preprint at arxiv.org: Link
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Grübel, R., Kabluchko, Z. (2015)
Edgeworth expansions for profiles of lattice branching random walks. Ann. Inst. H. Poincare, 53(4), pp. 2103-2134, 2017.
Preprint at arxiv.org: Link
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Kabluchko, Z., Lifshits, M. (2015)
Least energy approximation for processes with stationary increments. J. Theor. Probab., 30(1), pp 268-296, 2017.
Preprint at arxiv.org: Link
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Engelke, S., Kabluchko, Z. (2014)
Max-stable processes and stationary systems of independent Lévy particles. Stoch. Proc. Appl., 125, p.4272-4299, 2015.
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Dombry, C., Kabluchko, Z. (2014)
Random tessellations associated with max-stable random fields. Bernoulli, 24(1), p. 30-52, 2018.
Preprint at arxiv.org: Link
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Grübel, R., Kabluchko, Z. (2014)
A functional central limit theorem for branching random walks, almost sure weak convergence, and applications to random trees. Ann. Appl. Probab., 26(6), pp. 3659-3698, 2016.
Preprint at arxiv.org: Link
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Kabluchko, Z., Zaporozhets, D. (2014)
Intrinsic volumes of Sobolev balls with applications to Brownian convex hulls. Trans. Amer. Math. Soc., 368 (2016), pp. 8873-8899.
Preprint at arxiv.org: Link
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Kabluchko, Z., Klimovsky, A. (2014)
Generalized Random Energy Model at complex temperatures. 109 pages. Submitted.
Preprint at arxiv.org: Link -
Kabluchko, Z., Wang, Y. (2012)
Limiting distribution for the maximal standardized increment of a random walk. Stoch. Proc. Appl., 124(9), p.2824-2867, 2014.
Preprint at arxiv.org: Link
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Engelke, S., Malinowski, A., Kabluchko, Z., Schlather, M. (2012)
Estimation of Hüsler-Reiss distributions and Brown-Resnick processes. J. Royal Statist. Soc. B., 77(1), p. 239-265, 2015.
Preprint at arxiv.org: Link
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Kabluchko, Z., Stoev, S. (2012)
Stochastic integral representations and classification of sum- and max-infinitely divisible processes. Bernoulli, 22(1), p. 107-142, 2016.
Preprint at arxiv.org: Link
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Kabluchko, Z. (2012)
Critical points of random polynomials with independent identically
distributed roots. Proc. Amer. Math. Soc., 143 (2015), 695-702.
Preprint at arxiv.org: Link
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Zaporozhets, D., Kabluchko, Z. (2012)
Random determinants, mixed volumes of ellipsoids, and zeros of Gaussian random fields. Zap. Nauchn. Sem. POMI 408, p.187-196, 2012 (Russian version) or Journal of Math. Sci. 199(2), p.168-173, 2014 (English version).
Preprint at arxiv.org: Link
Publisher's homepage: Link (Russian version) or Link (English version). -
Kabluchko, Z., Zaporozhets, D. (2012)
Asymptotic distribution of complex zeros of random analytic functions. Ann. Probab., 42(4), p.1374-1395, 2014.
Preprint at arxiv.org (new, short version): Link
Preprint at arxiv.org (old, long version): Link
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Engelke, S., Kabluchko, Z., Schlather, M. (2012).
Maxima of independent, non-identically distributed Gaussian vectors. Bernoulli, 21(1), p. 38-61, 2015.
Preprint at arxiv.org: Link
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Kabluchko, Z., Klimovsky, A. (2012).
Complex random energy model: Zeros and fluctuations. Probab. Th. Related Fields., 158 (2014), pp. 159-196.
Publisher's homepage: Link
Preprint at arxiv.org: Link -
Kabluchko, Z., Zaporozhets, D. (2011).
Roots of random polynomials whose coefficients have logarithmic tails. Ann. Probab., 41(5), 2013, pp. 3542-3581.
Publisher's homepage: Link
Preprint at arxiv.org: Link -
Kabluchko, Z. (2011).
Persistence and equilibria of branching populations with exponential intensity. J. Appl. Probab., 49(1), p. 226-244, 2012.
Preprint at arxiv.org: Link
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Kabluchko, Z., Padoan, S.A. (2010).
Maxima of bivariate random vectors with strongly dependent Cauchy marginals. Unpublished. -
Kabluchko, Z. (2010).
The maximum of the Gaussian 1/f^alpha-noise in the case alpha<1. Unpublished.
Preprint at arxiv.org: Link -
Engelke, S., Kabluchko, Z., Schlather, M. (2010).
An equivalent representation of the Brown-Resnick process. Statist. Probab. Letters, 81, p. 1150-1154, 2011.
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Kabluchko, Z. (2011).
Extremes of the standardized Gaussian noise. Stoch. Processes. Appl. 121(3) p. 515-533.
Preprint at arxiv.org: Link
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Hashorva, E., Kabluchko, Z., Wübker, A. (2010).
Extremes of independent chi-square random vectors. Extremes 15(1) p. 35-42.
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Kabluchko, Z. (2010).
Distribution of levels in high-dimensional random landscapes. Ann. Appl. Probab. 22(1) p. 337-362.
Preprint at arxiv.org: Link
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Kabluchko, Z. (2010).
Functional limit theorems for sums of independent geometric Lévy processes. Bernoulli 17(3) p. 942-968.
Preprint at arxiv. org: Link
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Kabluchko, Z. (2010).
Limit laws for sums of independent random products: the lattice case. J. Theor. Probab. 25(2), p. 424-437
Preprint at arxiv.org: Link
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Kabluchko, Z. (2009).
Extremes of independent Gaussian processes. Extremes 14(3) p. 285-310.
Preprint at arxiv.org: Link
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Kabluchko, Z., Schlather, M. (2010).
Ergodic properties of max-infinitely divisible processes. Stoch. Processes Appl., 120, 281-295.
Preprint at arxiv.org: Link
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Kabluchko, Z. (2009).
Limiting distributions for sums of independent random products. Not published.
Preprint at arxiv.org: Link -
Kabluchko, Z. (2010).
Stationary systems of Gaussian processes. Ann. Appl. Probab., 20(6), 2295-2317.
Preprint at arxiv.org: Link
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Oesting, M., Kabluchko, Z. und Schlather, M. (2012).
Simulation of Brown-Resnick processes. Extremes, 15(1), 89-107.
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Hotz, T., Marnitz, P., Stichtenoth, R., Davies, L., Kabluchko, Z. and Munk, A. (2009). Locally adaptive image denoising by a statistical multiresolution criterion. Comput. Stat. Data Analysis, 56(3) p. 543-558, 2012.
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Preprint at arxiv.org: Link -
Wübker, A., Kabluchko, Z. (2009).
L2-spectral gaps, weak-reversible and very weak-reversible Markov chains.
Preprint at arxiv.org: Link -
Ballani, F., Kabluchko, Z., Schlather, M. (2009, appeared 2012).
Random marked sets. Adv. Appl. Probab., 44(3), 603-616.
Preprint at arxiv. org: Link
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Kabluchko, Z. (2009).
Extremes of space-time Gaussian processes Stoch. Processes Appl., 119, 3962-3980.
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Kabluchko, Z., Spodarev, E. (2009).
Scan statistic of Lévy noises and marked empirical processes. Adv. Appl. Probab., 41, 013-037.
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Kabluchko, Z. (2009).
Limiting distribution of the continuity modulus for Gaussian processes with stationary increments. Statist. Probab. Lett., 79, 953-956.
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Kabluchko, Z. (2009).
Spectral representations of sum- and max-stable processes. Extremes, 12, 401-424.
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Kabluchko, Z., Schlather, M., de Haan, L. (2009).
Stationary max-stable fields associated to negative definite functions. Ann. Probab. 37, 2042-2065.
Preprint at arxiv.org: Link
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Kabluchko, Z., Munk, A. (2009).
Shao's theorem on the maximum of standardized random walk increments for multidimensional arrays. ESAIM Probab. Stat. 13, 409-416.
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Kabluchko, Z., Munk, A. (2008).
Exact convergence rate for the maximum of standardized Gaussian increments. Elect. Comm. Probab., 13, 302-310.
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Kabluchko, Z. (2007).
Extreme-value analysis of standardized Gaussian increments. Not published.
Preprint at arxiv.org: Link
Erratum (21.06.2021): The numerical value of the constant $H$ given on page 32 is incorrect by a factor of 4. We thank Piotr Fryzlewicz for pointing this out. Numerical computations suggest that H is contained between 0.855 and 0.860. -
Denker, M., Kabluchko, Z. (2007).
An Erdös-Rényi law for mixing processes. Probab. Math. Stat., 27, 139-149.
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Kabluchko, Z., Proskurin, D., Samojlenko, Y. (2004).
On C*-algebras generated by deformations of the CCR. Ukr. Math. J., 56, 1813-1827.
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Kim, C. S., Proskurin, D., Iksanov, A., Kabluchko, Z. (2003).
The generalized CCR: representations and enveloping C*-algebra. Rev. Math. Phys., 15, 313-338.
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Kabluchko, Z. (2001).
On an extension of higher-dimensional noncommutative tori.
Meth. Func. Anal. Topol., 7, 28-33.
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Theses
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PhD Thesis. Kabluchko, Z. (2007).
Extreme-Value Analysis of Self-Normalized Increments. Available at the homepage of the University of Göttingen: Link -
Diploma Thesis. Kabluchko, Z. (2004).
Stochastische Löwner-Evolution. University of Göttingen.
Reviews
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