Research Interests

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.

Selected Publications

Selected Publications of Zakhar Kabluchko

$\bullet$ Z. Kabluchko, V. Vysotsky, and D. Zaporozhets. Convex hulls of random walks, hyperplane arrangements, and Weyl chambers. Geom. Funct. Anal. (GAFA), 27(4):880–918, 2017.

$\bullet$ Z. Kabluchko , V. Vysotsky, and D. Zaporozhets. Convex hulls of random walks: Expected number of faces and face probabilities. Advances in Math., 320(7):595–629, 2017.

$\bullet$ G. Alsmeyer, Z. Kabluchko, and A. Marynych. A leader-election procedure using records. Ann. Probab., 45(6B):4348–4388, 2017.

$\bullet$ Z. Kabluchko and D. Zaporozhets. Intrinsic volumes of Sobolev balls with applications to Brownian convex hulls. Trans. Amer. Math. Soc., 368:8873–8899, 2016.

$\bullet$ R. Grübel and Z. Kabluchko. A functional central limit theorem for branching random walks, almost sure weak convergence, and applications to random trees. Ann. Appl. Probab., 26(6):3659–3698, 2016.

$\bullet$ Z. Kabluchko. Critical points of random polynomials with independent identically distributed roots. Proc. Amer. Math. Soc, 143:695–702, 2015.

$\bullet$ Z. Kabluchko and D. Zaporozhets. Asymptotic distribution of complex zeros of random analytic functions. Ann. Probab., 42(4):1374–1395, 2014.

$\bullet$ Z. Kabluchko and A. Klimovsky. Complex random energy model: zeros and fluctuations. Probab. Theory Rel. Fields, 158(1-2):159–196, 2014.

$\bullet$ Z. Kabluchko and D. Zaporozhets. Roots of random polynomials whose coefficients have logarithmic tails. Ann. Probab., 41(5):3542–3581, 2013.

$\bullet$ Z. Kabluchko, M. Schlather, and L. de Haan. Stationary max-stable fields associated to negative definite functions. Ann. Probab., 37(5):2042–2065, 2009.

Current Publications

Current Publications

$\bullet $ Zakhar Kabluchko. Face numbers of high-dimensional Poisson zero cells. Proc. Amer. Math. Soc., August 2022. doi:10.1090/proc/16085.

$\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, 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 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 $ 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 $ 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 and Alexander Marynych. Lah distribution: Stirling numbers, records on compositions, and convex hulls of high-dimensional random walks. Probab. Theory Relat. Fields, May 2022. doi:10.1007/s00440-022-01146-9.

$\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 $ 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. 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 $ Zakhar Kabluchko. On expected face numbers of random beta and beta’ polytopes. Beitr. Algebra Geom., February 2022. doi:10.1007/s13366-022-00626-2.

$\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 $ 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.

$\bullet $ Anna Gusakova, Zakhar Kabluchko, and Christoph Thäle. The β-Delaunay tessellation II: The Gaussian limit tessellation. Electron. J. Probab., 27(none):1–33, January 2022. doi:10.1214/22-EJP782.

$\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 $ 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 $ 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 $ Samuel G. G. Johnston, Zakhar Kabluchko, and Joscha Prochno. Projections of the uniform distribution on the cube: A large deviation perspective. Studia Math., 264:103–119, December 2021. doi:10.4064/sm210413-16-9.

$\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. Recursive Scheme for Angles of Random Simplices, and Applications to Random Polytopes. Discrete Comput. Geom., 66(3):902–937, December 2021. doi:10.1007/s00454-020-00259-z.

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

$\bullet $ 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.

$\bullet $ Zakhar Kabluchko. Face numbers of high-dimensional Poisson zero cells. arXiv e-prints, October 2021. arXiv:2110.08201.

$\bullet $ Zakhar Kabluchko. Recursive scheme for angles of random simplices, and applications to random polytopes. Discret. Comp. Geom., 66(3):902–937, October 2021. doi:10.1007/s00454-020-00259-z.

$\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 $ Thomas Godland, Zakhar Kabluchko, and Christoph Thäle. Beta-star polytopes and hyperbolic stochastic geometry. arXiv e-prints, September 2021. arXiv:2109.01035.

$\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 $ Anna Gusakova, Zakhar Kabluchko, and Christoph Thäle. The β-Delaunay tessellation IV: mixing properties and central limit theorems. arXiv e-prints, August 2021. arXiv:2108.09472.

$\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 $ 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 $ 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. On expected face numbers of random beta and beta' polytopes. arXiv e-prints, July 2021. arXiv:2107.06655.

$\bullet $ Thomas Godland, Zakhar Kabluchko, and Christoph Thäle. Random cones in high dimensions II: Weyl cones. arXiv e-prints, June 2021. arXiv:2106.07244.

$\bullet $ Zakhar Kabluchko and Alexander Marynych. Lah distribution: Stirling numbers, records on compositions, and convex hulls of high-dimensional random walks. arXiv e-prints, May 2021. arXiv:2105.11365.

$\bullet $ Thomas Godland and Zakhar Kabluchko. Positive hulls of random walks and bridges. arXiv e-prints, April 2021. arXiv:2104.05542.

$\bullet $ Anna Gusakova, Zakhar Kabluchko, and Christoph Thäle. The β-Delaunay tessellation III: Kendall's problem and limit theorems in high dimensions. arXiv e-prints, April 2021. arXiv:2104.07348.

$\bullet $ Alexander Iksanov, Zakhar Kabluchko, and Valeriya Kotelnikova. A functional limit theorem for nested Karlin's occupancy scheme generated by discrete Weibull-like distributions. arXiv e-prints, April 2021. arXiv:2104.06948.

$\bullet $ Samuel G. G. Johnston, Zakhar Kabluchko, and Joscha Prochno. Projections of the uniform distribution on the cube – a large deviation perspective. arXiv e-prints, March 2021. arXiv:2103.16430.

$\bullet $ Zakhar Kabluchko. Angles of random simplices and face numbers of random polytopes. Advances in Mathematics, March 2021. doi:10.1016/j.aim.2021.107612.

$\bullet $ Zakhar Kabluchko and Joscha Prochno. The maximum entropy principle and volumetric properties of Orlicz balls. Journal of Mathematical Analysis and Applications, March 2021. doi:10.1016/j.jmaa.2020.124687.

$\bullet $ Zakhar Kabluchko, Andrea Sartori, and Igor Wigman. Expected nodal volume for non-Gaussian random band-limited functions. arXiv e-prints, February 2021. arXiv:2102.11689.

$\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. Proceedings of the American Mathematical Society, 149(1):355–367, January 2021. doi:10.1090/proc/15232.

$\bullet $ Anna Gusakova, Zakhar Kabluchko, and Christoph Thäle. The β-Delaunay tessellation II: the Gaussian limit tessellation. arXiv e-prints, January 2021. arXiv:2101.11316.

$\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, 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 $ 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 $ 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 $ 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 $ 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 $ Thomas Godland and Zakhar Kabluchko. Projections and angle sums of permutohedra and other polytopes. arXiv e-prints, September 2020. arXiv:2009.04186v1.

$\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-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.

$\bullet $ Zakhar Kabluchko. An identity for the coefficients of characteristic polynomials of hyperplane arrangements. arXiv e-prints, August 2020. arXiv:2008.06719.

$\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 and Zakhar Kabluchko. Angle sums of Schläfli orthoschemes. arXiv e-prints, July 2020. arXiv:2007.02293.

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

$\bullet $ Anna Gusakova, Zakhar Kabluchko, and Christoph Thäle. The β-Delaunay tessellation I: description of the model and geometry of typical cells. arXiv e-prints, May 2020. arXiv:2005.13875.

$\bullet $ Anastas Baci, Zakhar Kabluchko, Joscha Prochno, Mathias Sonnleitner, and Christoph Thaele. Limit theorems for random points in a simplex. arXiv e-prints, May 2020. arXiv:2005.04911v1.

$\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 $ Zakhar Kabluchko, Daniel Temesvari, and Christoph Thäle. A new approach to weak convergence of random cones and polytopes. arXiv e-prints, March 2020. arXiv:2003.04001.

$\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 $ Friedrich Götze, Zakhar Kabluchko, and Dmitry Zaporozhets. Grassmann angles and absorption probabilities of Gaussian convex hulls. arXiv e-prints, November 2019. arXiv:1911.04184.

$\bullet $ Zakhar Kabluchko and Mikhail A. Lifshits. Adaptive energy-saving approximation for stationary processes. Izvestiya: Mathematics, 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. Journal of Statistical Physics, 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. Transactions of the American Mathematical Society, 372(7):4585–4603, July 2019. doi:10.1090/tran/7871.

$\bullet $ Zakhar Kabluchko. Angles of random simplices with applications to random polytopes. arXiv e-prints, July 2019. arXiv:1907.07534.

$\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, Joscha Prochno, and Christoph Thäle. High-dimensional limit theorems for random vectors in $l_p^n$-balls. II. arXiv e-prints, June 2019. arXiv:1906.03599.

$\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 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, 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 $ 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, 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 $ 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.