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

$\bullet $ Z. Kabluchko, J. Prochno, and C. 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 $ A. Baci, Z. Kabluchko, J. Prochno, M. Sonnleitner, and C. Thaele. Limit theorems for random points in a simplex. arXiv e-prints, May 2020. arXiv:2005.04911v1.

$\bullet $ Z. Kabluchko and C. Thäle. Faces in random great hypersphere tessellations. arXiv e-prints, May 2020. arXiv:2005.01055.

$\bullet $ Z. Kabluchko, J. Prochno, and V. 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 $ T. Godland and Z. Kabluchko. Conical tessellations associated with Weyl chambers. arXiv e-prints, April 2020. arXiv:2004.10466.

$\bullet $ Z. Kabluchko, D. Temesvari, and C. Thäle. A new approach to weak convergence of random cones and polytopes. arXiv e-prints, March 2020. arXiv:2003.04001.

$\bullet $ H. Flasche and Z. 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 $ Z. Kabluchko, M. Löwe, and K. Schubert. Fluctuations for the partition function of Ising models on Erdös-Rényi random graphs. arXiv e-prints, February 2020. arXiv:2002.11372.

$\bullet $ Z. 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 $ Z. Kabluchko, A. Marynych, D. Temesvari, and C. 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 $ Z. Kabluchko and C. Thaele. The typical cell of a Voronoi tessellation on the sphere. arXiv e-prints, November 2019. arXiv:1911.07221.

$\bullet $ Z. Kabluchko, M. Löwe, and K. Schubert. Fluctuations of the Magnetization for Ising Models on Erdős-Rényi Random Graphs – the Regimes of Small p and the Critical Temperature. arXiv e-prints, November 2019. arXiv:1911.10624.

$\bullet $ F. Götze, Z. Kabluchko, and D. Zaporozhets. Grassmann angles and absorption probabilities of Gaussian convex hulls. arXiv e-prints, November 2019. arXiv:1911.04184.

$\bullet $ G. Bonnet, Z. Kabluchko, and N. Turchi. Phase transition for the volume of high-dimensional random polytopes. arXiv e-prints, November 2019. arXiv:1911.12696.

$\bullet $ Z. A. Kabluchko and M. A. Lifshits. Adaptive energy-saving approximation for stationary processes. Izvestiya: Mathematics, 83(5):932–956, October 2019. doi:10.1070/IM8840.

$\bullet $ Z. Kabluchko, J. Prochno, and C. Thaele. A new look at random projections of the cube and general product measures. arXiv e-prints, October 2019. arXiv:1910.02676.

$\bullet $ Z. Kabluchko. Angles of Random Simplices and Face Numbers of Random Polytopes. arXiv e-prints, September 2019. arXiv:1909.13335.

$\bullet $ G. Alsmeyer, Z. Kabluchko, A. Marynych, and V. Vysotsky. How long is the convex minorant of a one-dimensional random walk? arXiv e-prints, September 2019. arXiv:1909.12322.

$\bullet $ I. Ibragimov, Z. Kabluchko, and M. Lifshits. Some extensions of linear approximation and prediction problems for stationary processes. Stochastic Process. Appl., 129(8):2758–2782, August 2019. doi:10.1016/

$\bullet $ Z. Kabluchko, M. Löwe, and K. 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 $ G. Alsmeyer, Z. Kabluchko, and A. 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 $ Z. Kabluchko. Angles of random simplices with applications to random polytopes. arXiv e-prints, July 2019. arXiv:1907.07534.

$\bullet $ Z. 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 $ D. Alonso-Gutiérrez, F. Besau, J. Grote, Z. Kabluchko, M. Reitzner, C. Thäle, B.-H. Vritsiou, and E. M. Werner. Asymptotic normality for random simplices and convex bodies in high dimensions. arXiv e-prints, June 2019. arXiv:1906.02471.

$\bullet $ Z. Kabluchko, J. Prochno, and C. Thäle. High-dimensional limit theorems for random vectors in $l_p^n$-balls. II. arXiv e-prints, June 2019. URL:, arXiv:1906.03599.

$\bullet $ Z. Kabluchko and H. 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 $ Z. Kabluchko, J. Prochno, and C. 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 $ J. Grote, Z. Kabluchko, and C. 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 $ Z. Kabluchko, V. Vysotsky, and D. 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 $ Z. Kabluchko and D. 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 $ Z. Kabluchko and I. Wigman. Asymptotics for the expected number of nodal components for random lemniscates. arXiv e-prints, February 2019. arXiv:1902.08424.

$\bullet $ Z. Kabluchko, D. Temesvari, and C. Thäle. Expected intrinsic volumes and facet numbers of random beta-polytopes. Math. Nachr., 292(1):79–105, January 2019. doi:10.1002/mana.201700255.

$\bullet $ Z. Kabluchko. Expected $f$-vector of the poisson zero polytope and random convex hulls in the half-sphere. arXiv e-prints, January 2019. URL:, arXiv:1901.10528.