5 papers · 1 filter
On the distribution patterns of zeros for random polynomials with regularly varying coefficients
Zakhar Kabluchko, Boris Khoruzhenko, Alexander Marynych
This paper investigates asymptotic distribution of complex zeros of random polynomials , as , where is a regularly varying funct…
On local large deviations for decoupled random walks
Dariusz Buraczewski, Alexander Iksanov, Alexander Marynych
A decoupled standard random walk is a sequence of independent random variables such that, for each , the distribution of is the same…
Zeros and exponential profiles of polynomials I: Limit distributions, finite free convolutions and repeated differentiation
Jonas Jalowy, Zakhar Kabluchko, Alexander Marynych
Given a sequence of polynomials with only nonpositive zeros, the aim of this article is to present a user-friendly approach for determining the limiting…
Almost periodic stochastic processes with applications to analytic number theory
Alexander Iksanov, Zakhar Kabluchko, Alexander Marynych
A classical fact of the theory of almost periodic functions is the existence of their asymptotic distributions. In probabilistic terms, this means that if is a Besicovitch almo…
Set-valued recursions arising from vantage-point trees
Congzao Dong, Alexander Marynych, Ilya Molchanov
We study vantage-point trees constructed using an independent sample from the uniform distribution on a fixed convex body in , where is an…