D. Zaporozhets

activity

20112026

most citedAsymptotic distribution of complex zeros of random analytic functions

78 citations · 138 across the 27 of their papers we have counts for

collaborators

Showing 2016Show all

4 papers · 1 filter

math.PR2016

Convex hulls of random walks: Expected number of faces and face probabilities

Zakhar Kabluchko, Vladislav Vysotsky, Dmitry Zaporozhets

Consider a sequence of partial sums $S_{i} = ξ_{1} + \dots + ξ_{i}$ , $1 \leq i \leq n$ , starting at $S_{0} = 0$ , whose increments $ξ_{1}, \dots, ξ_{n}$ are random vectors in $R^{d}$ , $d \leq n$ . We…

math.PR2016

Correlations between real and complex zeros of a random polynomial

Friedrich Götze, Denis Koleda, Dmitry Zaporozhets

Consider a random polynomial $G (z) := ξ_{0} + ξ_{1} z + \dots + ξ_{n} z^{n}, z \in C,$ where $ξ_{0}, ξ_{1}, \dots, ξ_{n}$ are independent real-valued random variables with probability densi…

math.PR2016

A multidimensional analogue of the arcsine law for the number of positive terms in a random walk

Zakhar Kabluchko, Vladislav Vysotsky, Dmitry Zaporozhets

Consider a random walk $S_{i} = ξ_{1} + \dots + ξ_{i}$ , $i \in N$ , whose increments $ξ_{1}, ξ_{2}, \dots$ are independent identically distributed random vectors in $R^{d}$ such that $…

math.PR2016

Inclusion-exclusion principles for convex hulls and the Euler relation

Zakhar Kabluchko, Günter Last, Dmitry Zaporozhets

Consider $n$ points $X_{1}, \dots, X_{n}$ in $R^{d}$ and denote their convex hull by $Π$ . We prove a number of inclusion-exclusion identities for the system of convex hulls $Π_I:=…