Research Interests
$\bullet$ Random analytic functions and random polynomials.
$\bullet$ Stochastic, convex and integral geometry.
$\bullet$ Random trees, branching random walks.
$\bullet$ Analysis of algorithms and discrete random structures.
$\bullet$ Extreme value theory, heavy tails.
$\bullet$ Stable, max-stable, infinitely divisible stochastic processes and ergodic theory.
$\bullet$ Statistical mechanics.
$\bullet$ Probabilistic number theory.
• Godland, Thomas; Kabluchko, Zakhar; Thäle, Christoph Beta-star polytopes and hyperbolic stochastic geometry. Advances in Mathematics Vol. 404 (A), 2022 online
• Kabluchko, Zakhar Expected f-vector of the Poisson zero polytope and random convex hulls in the half-sphere. Mathematika Vol. 66 (4), 2020, pp 1028-1053 online
• Kabluchko, Zakhar Angles of random simplices and face numbers of random polytopes. Advances in Mathematics Vol. 380, 2021, pp Paper No. 107612, 68 online
• Kabluchko, Zakhar; Marynych, Alexander Lah distribution: Stirling numbers, records on compositions, and convex hulls of high-dimensional random walks. Probability Theory and Related Fields Vol. 184 (3-4), 2022 online
• Kabluchko, Zakhar; Marynych, Alexander; Temesvari, David, Thäle; Christoph Cones generated by random points on half-spheres and convex hulls of Poisson point processes. Probability Theory and Related Fields Vol. 175 (3-4), 2019, pp 1021-1061 online
• Kabluchko, Zakhar; Schlather, Martin, de Haan, Laurens Stationary max-stable fields associated to negative definite functions. Annals of Probability Vol. 37 (5), 2009, pp 2042-2065 online
• Kabluchko, Zakhar; Thäle, Christoph; Zaporozhets, Dmitry Beta polytopes and Poisson polyhedra: f-vectors and angles. Advances in Mathematics Vol. 374, 2020, pp 107333, 63 online
• Kabluchko, Zakhar; Vysotsky, Vladislav; Zaporozhets, Dmitry Convex hulls of random walks, hyperplane arrangements, and Weyl chambers. Geometric And Functional Analysis Vol. 27 (4), 2017, pp 880-918 online
• Kabluchko, Zakhar; Vysotsky, Vladislav; Zaporozhets, Dmitry Convex hulls of random walks: Expected number of faces and face probabilities. Advances in Mathematics Vol. 320 (7), 2017, pp 595-629 online
• Kabluchko, Zakhar; Zaporozhets, Dmitry Asymptotic distribution of complex zeros of random analytic functions. Annals of Probability Vol. 42 (4), 2014, pp 1374-1395 online
Recent Publications of Prof. Dr. Zakhar Kabluchko
$\bullet $ Alexander Iksanov, Zakhar Kabluchko, and Alexander Marynych. Almost periodic stochastic processes with applications to analytic number theory. arXiv e-prints, February 2025. arXiv:2502.04969.
$\bullet $ Zakhar Kabluchko and Hugo Panzo. A refinement of the Sylvester problem: Probabilities of combinatorial types. arXiv e-prints, January 2025. arXiv:2501.16166.
$\bullet $ Anna Gusakova and Zakhar Kabluchko. Sylvester's problem for beta-type distributions. arXiv e-prints, January 2025. arXiv:2501.00671.
$\bullet $ Zakhar Kabluchko and Mathias Sonnleitner. Strange shadows of $\ell _p$-balls. arXiv e-prints, December 2024. arXiv:2412.17475.
$\bullet $ Zakhar Kabluchko and Matthias Löwe. Propagation of chaos in the random field Curie–Weiss model. Journal of Statistical Mechanics: Theory and Experiment, 2024(11):113206, November 2024. doi:10.1088/1742-5468/ad8f2a.
$\bullet $ Jonas Jalowy, Zakhar Kabluchko, and Matthias Löwe. Propagation of chaos and residual dependence in gibbs measures on finite sets. arXiv e-prints, October 2024. arXiv:2410.08004.
$\bullet $ Anna Gusakova, Zakhar Kabluchko, and Christoph Thäle. Sectional Voronoi tessellations: characterization and high-dimensional limits. Bernoulli, May 2024. doi:10.3150/23-bej1641.
$\bullet $ Michael Juhos, Zakhar Kabluchko, and Joscha Prochno. Asymptotic theory of schatten classes. arXiv e-prints, April 2024. arXiv:2404.07145.
$\bullet $ Gerold Alsmeyer, Alexander Iksanov, and Zakhar Kabluchko. On decoupled standard random walks. arXiv e-prints, February 2024. arXiv:2402.05488.
$\bullet $ Matthias Löwe and Zakhar Kabluchko. Propagation of chaos in the random field curie-weiss model. arXiv e-prints, December 2023. arXiv:2312.01866.
$\bullet $ Zakhar Kabluchko and Alexander Marynych. Divisibility properties of polynomial expressions of random integers. arXiv e-prints, November 2023. arXiv:2311.05369.
$\bullet $ Jeremy Hoskins and Zakhar Kabluchko. Dynamics of zeroes under repeated differentiation. Experimental Mathematics, 32(4):573–599, October 2023. doi:10.1080/10586458.2021.1980752.
$\bullet $ Zakhar Kabluchko. An identity for the coefficients of characteristic polynomials of hyperplane arrangements. Discrete &; Computational Geometry, 70(4):1476–1498, October 2023. doi:10.1007/s00454-023-00577-y.
$\bullet $ Zakhar Kabluchko and David Albert Steigenberger. $r$-Lah distribution: Properties, limit theorems and an application to compressed sensing. Advances in Applied Mathematics, 150:102575, September 2023. doi:10.1016/j.aam.2023.102575.
$\bullet $ Zakhar Kabluchko, Alexander Marynych, and Kilian Raschel. Multivariate multiplicative functions of uniform random vectors in large integer domains. Results in Mathematics, 78(5):201, August 2023. doi:10.1007/s00025-023-01978-4.
$\bullet $ Brian C. Hall, Ching-Wei Ho, Jonas Jalowy, and Zakhar Kabluchko. Zeros of random polynomials undergoing the heat flow. arXiv e-prints, August 2023. arXiv:2308.11685.
$\bullet $ Friedrich Götze, Zakhar Kabluchko, and Dmitry Zaporozhets. Grassmann angles and absorption probabilities of Gaussian convex hulls. Journal of Mathematical Sciences, 273(5):738–754, July 2023. doi:10.1007/s10958-023-06537-4.
$\bullet $ Zakhar Kabluchko, Alexander Marynych, and Kilian Raschel. Random walks in the high-dimensional limit II: The crinkled subordinator. arXiv e-prints, June 2023. arXiv:2306.04747.
$\bullet $ Brian Hall, Ching-Wei Ho, Jonas Jalowy, and Zakhar Kabluchko. The heat flow, GAF, and SL(2;R). arXiv e-prints, April 2023. doi:2304.06665.
$\bullet $ Thomas Godland and Zakhar Kabluchko. Projections and angle sums of belt polytopes and permutohedra. Results in Mathematics, 78(4):140, April 2023. doi:10.1007/s00025-023-01918-2.
$\bullet $ Zakhar Kabluchko, Daniel Rosen, and Christoph Thäle. A quantitative central limit theorem for Poisson horospheres in high dimensions. arXiv e-prints, March 2023. arXiv:2303.17827.
$\bullet $ Zakhar Kabluchko, Joscha Prochno, and Mathias Sonnleitner. A probabilistic approach to Lorentz balls. arXiv e-prints, March 2023. arXiv:2303.04728.
$\bullet $ Anna Gusakova, Zakhar Kabluchko, and Christoph Thäle. The β-Delaunay tessellation IV: mixing properties and central limit theorems. Stochastics and Dynamics, February 2023. doi:10.1142/s0219493723500211.
$\bullet $ Christoph Aistleitner, Nina Gantert, Zakhar Kabluchko, Joscha Prochno, and Kavita Ramanan. Large deviation principles for lacunary sums. Transactions of the American Mathematical Society, 376(01):507–553, January 2023. doi:10.1090/tran/8788.
$\bullet $ Anna Gusakova, Zakhar Kabluchko, and Christoph Thäle. Sectional Voronoi tessellations: Characterization and high-dimensional limits. arXiv e-prints, January 2023. arXiv:2301.03297.
$\bullet $ Jonas Jalowy, Zakhar Kabluchko, Matthias Löwe, and Alexander Marynych. When does the chaos in the Curie-Weiss model stop to propagate? Electronic Journal of Probability, January 2023. doi:10.1214/23-ejp1039.
$\bullet $ Alexander Iksanov, Zakhar Kabluchko, and Valeriya Kotelnikova. A law of the iterated logarithm for iterated random walks, with application to random recursive trees. arXiv e-prints, December 2022. arXiv:2212.13441.
$\bullet $ Zakhar Kabluchko and Alexander Marynych. Random walks in the high-dimensional limit I. arXiv e-prints, November 2022. arXiv:2211.08538.
$\bullet $ Anastas Baci, Zakhar Kabluchko, Joscha Prochno, Mathias Sonnleitner, and Christoph Thäle. Limit theorems for random points in a simplex. J. Appl. Probab., 59(3):685–701, September 2022. doi:10.1017/jpr.2021.77.
$\bullet $ Zakhar Kabluchko, Alexander Marynych, and Helmut Pitters. Mod-ϕ convergence of Stirling distributions and limit theorems for zeros of their generating functions. arXiv e-prints, September 2022. arXiv:2209.06808.
$\bullet $ Michael Juhos, Zakhar Kabluchko, and Joscha Prochno. Limit theorems for mixed-norm sequence spaces with applications to volume distribution. arXiv e-prints, September 2022. arXiv:2209.08937.
$\bullet $ Zakhar Kabluchko, Matthias Löwe, and Kristina Schubert. Fluctuations of the magnetization for ising models on Erdős-Rényi random graphs – the regimes of low temperature and external magnetic field. Lat. Am. J. Probab. Math. Stat, 19:537––563, August 2022. doi:10.30757/ALEA.v19-21.
$\bullet $ Thomas Godland, Zakhar Kabluchko, and Christoph Thäle. Beta-star polytopes and hyperbolic stochastic geometry. Adv. Math., 404:108382, August 2022. doi:10.1016/j.aim.2022.108382.
$\bullet $ Zakhar Kabluchko. Face numbers of high-dimensional Poisson zero cells. Proc. Amer. Math. Soc., 151(1):401–415, August 2022. doi:10.1090/proc/16085.
$\bullet $ Anna Gusakova, Zakhar Kabluchko, and Christoph Thäle. The β-Delaunay tessellation: Description of the model and geometry of typical cells. Adv. Appl. Probab., 54(4):1252–1290, August 2022. doi:10.1017/apr.2022.6.
$\bullet $ Thomas Godland and Zakhar Kabluchko. Angle sums of Schläfli orthoschemes. Discret. Comp. Geom., 68(1):125–164, July 2022. doi:10.1007/s00454-021-00326-z.
$\bullet $ Thomas Godland and Zakhar Kabluchko. Conic intrinsic volumes of Weyl chambers. Mod. Stoch.: Theory Appl., 9(3):357–375, June 2022. doi:10.15559/22-VMSTA206.
$\bullet $ Thomas Godland and Zakhar Kabluchko. Positive hulls of random walks and bridges. Stoch. Process. Their Appl., 147:327–362, May 2022. doi:10.1016/j.spa.2022.01.019.
$\bullet $ Zakhar Kabluchko, Daniel Rosen, and Christoph Thäle. Fluctuations of λ-geodesic Poisson hyperplanes in hyperbolic space. arXiv e-prints, May 2022. arXiv:2205.12820.
$\bullet $ Zakhar Kabluchko and Alexander Marynych. Lah distribution: Stirling numbers, records on compositions, and convex hulls of high-dimensional random walks. Probab. Theory Relat. Fields, 184(3–4):969–1028, May 2022. doi:10.1007/s00440-022-01146-9.
$\bullet $ Thomas Godland, Zakhar Kabluchko, and Christoph Thäle. Random cones in high dimensions II: Weyl cones. Mathematika, 68(3):710–737, April 2022. doi:10.1112/mtk.12136.
$\bullet $ Zakhar Kabluchko and Hauke Seidel. Convex cones spanned by regular polytopes. Adv. Geom., 22(2):245–267, April 2022. doi:10.1515/advgeom-2021-0041.
$\bullet $ Zakhar Kabluchko. Lee-Yang zeroes of the Curie-Weiss ferromagnet, unitary Hermite polynomials, and the backward heat flow. arXiv e-prints, March 2022. arXiv:2203.05533.
$\bullet $ Alexander Iksanov, Zakhar Kabluchko, and Valeriya Kotelnikova. A functional limit theorem for nested Karlin's occupancy scheme generated by discrete Weibull-like distributions. J. Math. Anal. Appl., 507(2):125798, March 2022. doi:10.1016/j.jmaa.2021.125798.
$\bullet $ Samuel G. G. Johnston, Zakhar Kabluchko, and Joscha Prochno. Projections of the uniform distribution on the cube: a large deviation perspective. Stud. Math., 264(1):103–119, March 2022. doi:10.4064/sm210413-16-9.
$\bullet $ Zakhar Kabluchko, Alexander Marynych, and Ilya Molchanov. Generalised convexity with respect to families of affine maps. arXiv e-prints, February 2022. arXiv:2202.07887.
$\bullet $ Zakhar Kabluchko. On expected face numbers of random beta and beta’ polytopes. Beitr. Algebra Geom., 64(1):155–174, February 2022. doi:10.1007/s13366-022-00626-2.
$\bullet $ Anna Gusakova, Zakhar Kabluchko, and Christoph Thäle. The β-Delaunay tessellation II: The Gaussian limit tessellation. Electron. J. Probab., 27:1–33, January 2022. doi:10.1214/22-EJP782.
$\bullet $ Zakhar Kabluchko and Igor Wigman. Asymptotics for the expected number of nodal components for random lemniscates. Int. Math. Res. Not., 2022(3):2337–2375, January 2022. doi:10.1093/imrn/rnaa146.
$\bullet $ Thomas Godland, Zakhar Kabluchko, and Christoph Thäle. Random cones in high dimensions I: Donoho-Tanner and Cover-Efron cones. Discret. Anal., January 2022. doi:10.19086/da.36223.
$\bullet $ Anna Gusakova, Zakhar Kabluchko, and Christoph Thäle. The β-Delaunay tessellation III: Kendall's problem and limit theorems in high dimensions. Lat. Am. J. Probab. Math. Stat., 19:23–50, January 2022. doi:10.30757/alea.v19-02.
$\bullet $ Zakhar Kabluchko, Daniel Temesvari, and Christoph Thäle. A new approach to weak convergence of random cones and polytopes. Canad. J. Math., 73(6):1627–1647, December 2021. doi:10.4153/S0008414X20000620.
$\bullet $ Zakhar Kabluchko. Repeated differentiation and free unitary Poisson process. arXiv e-prints, December 2021. arXiv:2112.14729.
$\bullet $ Zakhar Kabluchko, Joscha Prochno, and Christoph Thäle. High-dimensional limit theorems for random vectors in $l_p^n$-balls. II. Commun. Contemp. Math., 23(03):1950073, November 2021. doi:10.1142/s0219199719500731.
$\bullet $ Zakhar Kabluchko, Matthias Löwe, and Kristina Schubert. Fluctuations for the partition function of Ising models on Erdös–Rényi random graphs. Ann. Inst. Henri Poincaré Probab. Stat., 57(4):2017–2042, November 2021. doi:10.1214/20-aihp1137.
$\bullet $ Zakhar Kabluchko and Joscha Prochno. Large deviations for random matrices in the orthogonal group and Stiefel manifold with applications to random projections of product distributions. arXiv e-prints, October 2021. arXiv:2110.12977.
$\bullet $ Zakhar Kabluchko, Joscha Prochno, and Christoph Thäle. A new look at random projections of the cube and general product measures. Bernoulli, 27(3):2117–2138, August 2021. doi:10.3150/20-bej1303.
$\bullet $ Thomas Godland and Zakhar Kabluchko. Conical tessellations associated with Weyl chambers. Trans. Amer. Math. Soc., 374(10):7161–7196, July 2021. doi:10.1090/tran/8445.
$\bullet $ Zakhar Kabluchko and Christoph Thäle. The typical cell of a Voronoi tessellation on the sphere. Discrete Comput. Geom., 66(4):1330–1350, July 2021. doi:10.1007/s00454-021-00315-2.
$\bullet $ Gilles Bonnet, Zakhar Kabluchko, and Nicola Turchi. Phase transition for the volume of high-dimensional random polytopes. Random Structures Algorithms, 58(4):648–663, July 2021. doi:10.1002/rsa.20986.
$\bullet $ Zakhar Kabluchko and Joscha Prochno. The maximum entropy principle and volumetric properties of Orlicz balls. J. Math. Anal. Appl., March 2021. doi:10.1016/j.jmaa.2020.124687.
$\bullet $ Zakhar Kabluchko. Angles of random simplices and face numbers of random polytopes. Adv. Math., March 2021. doi:10.1016/j.aim.2021.107612.
$\bullet $ Zakhar Kabluchko and Christoph Thäle. Faces in random great hypersphere tessellations. Electron. J. Probab., 26:Paper No. 3, 35, January 2021. doi:10.1214/20-ejp570.
$\bullet $ David Alonso-Gutiérrez, Florian Besau, Julian Grote, Zakhar Kabluchko, Matthias Reitzner, Christoph Thäle, Beatrice-Helen Vritsiou, and Elisabeth Werner. Asymptotic normality for random simplices and convex bodies in high dimensions. Proc. Amer. Math. Soc., 149(1):355–367, January 2021. doi:10.1090/proc/15232.
$\bullet $ Zakhar Kabluchko and Dmitry Zaporozhets. Angles of the Gaussian simplex. J. Math. Sci., 251(4):480–488, December 2020. doi:10.1007/s10958-020-05107-2.
$\bullet $ Zakhar Kabluchko. Recursive scheme for angles of random simplices, and applications to random polytopes. Discrete Comput. Geom., 66(3):902–937, December 2020. doi:10.1007/s00454-020-00259-z.
$\bullet $ Hendrik Flasche and Zakhar Kabluchko. Expected number of real zeroes of random Taylor series. Commun. Contemp. Math., 22(7):1950059, 38, November 2020. doi:10.1142/S0219199719500597.
$\bullet $ Zakhar Kabluchko, Christoph Thäle, and Dmitry Zaporozhets. Beta polytopes and Poisson polyhedra: $f$-vectors and angles. Adv. Math., 374:107333, 63, November 2020. doi:10.1016/j.aim.2020.107333.
$\bullet $ Zakhar Kabluchko, Joscha Prochno, and Christoph Thäle. Intersection of unit balls in classical matrix ensembles. Israel J. Math., 239(1):129–172, October 2020. doi:10.1007/s11856-020-2052-6.
$\bullet $ Friedrich Götze, Anna Gusakova, Zakhar Kabluchko, and Dmitry Zaporozhets. Distribution of complex algebraic numbers on the unit circle. Journal of Mathematical Sciences, 251(1):54–66, October 2020. doi:10.1007/s10958-020-05064-w.
$\bullet $ Gerold Alsmeyer, Zakhar Kabluchko, Alexander Marynych, and Vladislav Vysotsky. How long is the convex minorant of a one-dimensional random walk? Electron. J. Probab., 25:Paper No. 105, 22, September 2020. doi:10.1214/20-ejp497.
$\bullet $ Zakhar Kabluchko, Joscha Prochno, and Christoph Thäle. Exact asymptotic volume and volume ratio of Schatten unit balls. J. Approx. Theory, 257:105457, 13, September 2020. doi:10.1016/j.jat.2020.105457.
$\bullet $ Zakhar Kabluchko, Matthias Löwe, and Kristina Schubert. Fluctuations of the magnetization for Ising models on Erdős-Rényi random graphs—the regimes of small $p$ and the critical temperature. J. Phys. A, 53(35):355004, 37, August 2020. doi:10.1088/1751-8121/aba05f.
$\bullet $ Zakhar Kabluchko. Expected $f$-vector of the Poisson zero polytope and random convex hulls in the half-sphere. Mathematika, 66(4):1028–1053, August 2020. doi:10.1112/mtk.12056.
$\bullet $ Zakhar Kabluchko and Dmitry Zaporozhets. Absorption probabilities for Gaussian polytopes and regular spherical simplices. Adv. in Appl. Probab., 52(2):588–616, July 2020. doi:10.1017/apr.2020.7.
$\bullet $ Thomas Godland, Zakhar Kabluchko, and Dmitry Zaporozhets. Angle sums of random polytopes. arXiv e-prints, July 2020. arXiv:2007.02590.
$\bullet $ Zakhar Kabluchko, Joscha Prochno, and Christoph Thäle. Sanov-type large deviations in Schatten classes. Annales de L'Institut Henri Poincare Section (B) Probability and Statistics, 56(2):928–953, May 2020. doi:10.1214/19-AIHP989.
$\bullet $ Zakhar Kabluchko, Joscha Prochno, and Vladislav Vysotsky. Yet another note on the arithmetic-geometric mean inequality. Studia Math., 253(1):39–55, April 2020. doi:10.4064/sm181014-16-3.
$\bullet $ Hendrik Flasche and Zakhar Kabluchko. Real zeroes of random analytic functions associated with geometries of constant curvature. J. Theoret. Probab., 33(1):103–133, March 2020. doi:10.1007/s10959-018-0843-z.
$\bullet $ Zakhar Kabluchko. Angle sums of random simplices in dimensions $3$ and $4$. Proc. Amer. Math. Soc., 148(7):3079–3086, February 2020. doi:10.1090/proc/14934.
$\bullet $ Zakhar Kabluchko, Alexander Marynych, Daniel Temesvari, and Christoph Thäle. Cones generated by random points on half-spheres and convex hulls of Poisson point processes. Probab. Theory Related Fields, 175(3-4):1021–1061, December 2019. doi:10.1007/s00440-019-00907-3.
$\bullet $ Zakhar Kabluchko and Mikhail A. Lifshits. Adaptive energy-saving approximation for stationary processes. Izv. Math., 83(5):932–956, October 2019. doi:10.1070/IM8840.
$\bullet $ Ildar Ibragimov, Zakhar Kabluchko, and Mikhail Lifshits. Some extensions of linear approximation and prediction problems for stationary processes. Stochastic Process. Appl., 129(8):2758–2782, August 2019. doi:10.1016/j.spa.2018.08.001.
$\bullet $ Zakhar Kabluchko, Matthias Löwe, and Kristina Schubert. Fluctuations of the magnetization for Ising models on dense Erdős–Rényi random graphs. J. Stat. Phys., 177(1):78–94, August 2019. doi:10.1007/s10955-019-02358-5.
$\bullet $ Gerold Alsmeyer, Zakhar Kabluchko, and Alexander Marynych. Limit theorems for the least common multiple of a random set of integers. Trans. Amer. Math. Soc., 372(7):4585–4603, July 2019. doi:10.1090/tran/7871.
$\bullet $ Zakhar Kabluchko. An infinite-dimensional helix invariant under spherical projections. Electron. Commun. Probab., 24:Paper No. 25, 13, June 2019. doi:10.1214/19-ECP234.
$\bullet $ Zakhar Kabluchko and Hauke Seidel. Distances between zeroes and critical points for random polynomials with i.i.d. zeroes. Electron. J. Probab., 24:Paper No. 34, 25, April 2019. doi:10.1214/19-EJP295.
$\bullet $ Zakhar Kabluchko, Joscha Prochno, and Christoph Thäle. High-dimensional limit theorems for random vectors in $\ell _p^n$-balls. Commun. Contemp. Math., 21(1):1750092, 30, February 2019. doi:10.1142/S0219199717500924.
$\bullet $ Zakhar Kabluchko and Dmitry Zaporozhets. Expected volumes of Gaussian polytopes, external angles, and multiple order statistics. Trans. Amer. Math. Soc., 372(3):1709–1733, February 2019. doi:10.1090/tran/7708.
$\bullet $ Zakhar Kabluchko, Vladislav Vysotsky, and Dmitry Zaporozhets. A multidimensional analogue of the arcsine law for the number of positive terms in a random walk. Bernoulli, 25(1):521–548, February 2019. doi:10.3150/17-bej996.
$\bullet $ Julian Grote, Zakhar Kabluchko, and Christoph Thäle. Limit theorems for random simplices in high dimensions. ALEA Lat. Am. J. Probab. Math. Stat., 16(1):141–177, February 2019. doi:10.30757/alea.v16-06.
$\bullet $ Zakhar Kabluchko, Daniel Temesvari, and Christoph Thäle. Expected intrinsic volumes and facet numbers of random beta-polytopes. Math. Nachr., 292(1):79–105, January 2019. doi:10.1002/mana.201700255.