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 and C. Thaele. The typical cell of a Voronoi tessellation on the sphere. arXiv e-prints, November 2019. arXiv:1911.07221.

$\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. 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 $ 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 $ 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. URL: https://ui.adsabs.harvard.edu/abs/2019JSP...tmp..177K, 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, J. Prochno, and C. Thäle. High-dimensional limit theorems for random vectors in $l_p^n$-balls. II. arXiv e-prints, June 2019. URL: https://ui.adsabs.harvard.edu/abs/2019arXiv190603599K, arXiv:1906.03599.

$\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. Angle sums of random simplices in dimensions $3$ and $4$. arXiv e-prints, May 2019. URL: https://ui.adsabs.harvard.edu/abs/2019arXiv190501533K, arXiv:1905.01533.

$\bullet $ Z. Kabluchko and I. Wigman. Asymptotics for the expected number of nodal components for random lemniscates. arXiv e-prints, February 2019. URL: https://ui.adsabs.harvard.edu/abs/2019arXiv190208424K, arXiv:1902.08424.

$\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: https://ui.adsabs.harvard.edu/abs/2019arXiv190110528K, arXiv:1901.10528.