Alexander Marynych

Weak Convergence of Finite-Dimensional Distributions of the Number of Empty Boxes in the Bernoulli Sieve

The Bernoulli sieve is a random allocation scheme obtained by placing independent points with the uniform

Local universality for real roots of random trigonometric polynomials

[0,1]

Asymptotics of random processes with immigration II: Convergence to stationarity

law into the intervals made up by successive positions of a multiplicative random walk with factors taking values in the interval

On perpetuities with gamma-like tails

(0,1)

A functional limit theorem for random processes with immigration in the case of heavy tails

. Assuming that the number of points is equal to

A leader-election procedure using records

n

General Edgeworth expansions with applications to profiles of random trees

we investigate weak convergence, as

Renewal approximation for the absorption time of a decreasing Markov chain

n\to\infty

On Λ-coalescents with dust component

, of finite-dimensional distributions of the number of empty intervals within the occupancy range. A new argument enables us to relax the constraints imposed in previous papers on the distribution of the factor of the multiplicative random walk.

Limit theorems for renewal shot noise processes with eventually decreasing response functions

Consider a random trigonometric polynomial