Research Interests

Research Interests

Random analytic functions and random polynomials.
Stochastic, convex and integral geometry.
Random trees, branching random walks.
Analysis of algorithms and discrete random structures.
Extreme value theory, heavy tails.
Stable, max-stable, infinitely divisible stochastic processes and ergodic theory.
Statistical mechanics.
Probabilistic number theory.

Selected Publications

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

Recent Publications of Prof. Dr. Zakhar Kabluchko

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.

Zakhar Kabluchko and Hugo Panzo. A refinement of the Sylvester problem: Probabilities of combinatorial types. arXiv e-prints, January 2025. arXiv:2501.16166.

Anna Gusakova and Zakhar Kabluchko. Sylvester's problem for beta-type distributions. arXiv e-prints, January 2025. arXiv:2501.00671.

Zakhar Kabluchko and Mathias Sonnleitner. Strange shadows of p-balls. arXiv e-prints, December 2024. arXiv:2412.17475.

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.

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.

Anna Gusakova, Zakhar Kabluchko, and Christoph Thäle. Sectional Voronoi tessellations: characterization and high-dimensional limits. Bernoulli, May 2024. doi:10.3150/23-bej1641.

Michael Juhos, Zakhar Kabluchko, and Joscha Prochno. Asymptotic theory of schatten classes. arXiv e-prints, April 2024. arXiv:2404.07145.

Gerold Alsmeyer, Alexander Iksanov, and Zakhar Kabluchko. On decoupled standard random walks. arXiv e-prints, February 2024. arXiv:2402.05488.

Matthias Löwe and Zakhar Kabluchko. Propagation of chaos in the random field curie-weiss model. arXiv e-prints, December 2023. arXiv:2312.01866.

Zakhar Kabluchko and Alexander Marynych. Divisibility properties of polynomial expressions of random integers. arXiv e-prints, November 2023. arXiv:2311.05369.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Zakhar Kabluchko, Joscha Prochno, and Mathias Sonnleitner. A probabilistic approach to Lorentz balls. arXiv e-prints, March 2023. arXiv:2303.04728.

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.

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.

Anna Gusakova, Zakhar Kabluchko, and Christoph Thäle. Sectional Voronoi tessellations: Characterization and high-dimensional limits. arXiv e-prints, January 2023. arXiv:2301.03297.

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.

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.

Zakhar Kabluchko and Alexander Marynych. Random walks in the high-dimensional limit I. arXiv e-prints, November 2022. arXiv:2211.08538.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Zakhar Kabluchko, Daniel Rosen, and Christoph Thäle. Fluctuations of λ-geodesic Poisson hyperplanes in hyperbolic space. arXiv e-prints, May 2022. arXiv:2205.12820.

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.

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.

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.

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.

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.

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.

Zakhar Kabluchko, Alexander Marynych, and Ilya Molchanov. Generalised convexity with respect to families of affine maps. arXiv e-prints, February 2022. arXiv:2202.07887.

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.

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.

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.

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.

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.

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.

Zakhar Kabluchko. Repeated differentiation and free unitary Poisson process. arXiv e-prints, December 2021. arXiv:2112.14729.

Zakhar Kabluchko, Joscha Prochno, and Christoph Thäle. High-dimensional limit theorems for random vectors in lnp-balls. II. Commun. Contemp. Math., 23(03):1950073, November 2021. doi:10.1142/s0219199719500731.

Zakhar Kabluchko, Matthias Löwe, and Kristina Schubert. Fluctuations for the partition function of Ising models on Erdös–nyi random graphs. Ann. Inst. Henri Poincaré Probab. Stat., 57(4):2017–2042, November 2021. doi:10.1214/20-aihp1137.

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.

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.

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.

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.

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.

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.

Zakhar Kabluchko. Angles of random simplices and face numbers of random polytopes. Adv. Math., March 2021. doi:10.1016/j.aim.2021.107612.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Zakhar Kabluchko, Matthias Löwe, and Kristina Schubert. Fluctuations of the magnetization for Ising models on Erdős-nyi 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.

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.

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.

Thomas Godland, Zakhar Kabluchko, and Dmitry Zaporozhets. Angle sums of random polytopes. arXiv e-prints, July 2020. arXiv:2007.02590.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Zakhar Kabluchko, Joscha Prochno, and Christoph Thäle. High-dimensional limit theorems for random vectors in np-balls. Commun. Contemp. Math., 21(1):1750092, 30, February 2019. doi:10.1142/S0219199717500924.

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.

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.

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.

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.