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## Cones generated by random points on half-spheres and convex hulls of Poisson point processes

- Z. Kabluchko, A. Marynych, Daniel Temesvari, C. Thäle
- MathematicsProbability Theory and Related Fields
- 24 January 2018

Let $$U_1,U_2,\ldots $$U1,U2,… be random points sampled uniformly and independently from the d-dimensional upper half-sphere. We show that, as $$n\rightarrow \infty $$n→∞, the f-vector of the… Expand

## On Λ-Coalescents with Dust Component

- A. Gnedin, A. Iksanov, A. Marynych
- Mathematics, PhysicsJournal of Applied Probability
- 1 December 2011

We consider the Λ-coalescent processes with a positive frequency of singleton clusters. The class in focus covers, for instance, the beta(a, b)-coalescents with a > 1. We show that some large-sample… Expand

## The Bernoulli sieve: an overview

- A. Gnedin, A. Iksanov, A. Marynych
- Mathematics
- 31 May 2010

The Bernoulli sieve is a version of the classical balls-in-boxes occupancy scheme, in which random frequencies of infinitely many boxes are produced by a multiplicative random walk, also known as the… Expand

## Local universality for real roots of random trigonometric polynomials

- A. Iksanov, Z. Kabluchko, A. Marynych
- Mathematics
- 21 January 2016

Consider a random trigonometric polynomial $X_n: \mathbb R \to \mathbb R$ of the form $$ X_n(t) = \sum_{k=1}^n \left( \xi_k \sin (kt) + \eta_k \cos (kt)\right), $$ where… Expand

## On the number of collisions in beta(2, b)-coalescents

- A. Iksanov, A. Marynych, Martin Mohle
- Mathematics
- 1 August 2009

Expansions are provided for the moments of the number of collisions $X_n$ in the $\beta(2,b)$-coalescent restricted to the set $\{1,...,n\}$. We verify that $X_n/\mathbb{E}X_n$ converges almost… Expand

## General Edgeworth expansions with applications to profiles of random trees

- Z. Kabluchko, A. Marynych, Henning Sulzbach
- Mathematics
- 13 June 2016

We prove an asymptotic Edgeworth expansion for the profiles of certain random trees including binary search trees, random recursive trees and plane-oriented random trees, as the size of the tree goes… Expand

## A Brownian weak limit for the least common multiple of a random m-tuple of integers

- D. Buraczewski, A. Iksanov, A. Marynych
- Mathematics
- 12 April 2020

Let $B_n(m)$ be a set picked uniformly at random among all $m$-elements subsets of $\{1,2,\ldots,n\}$. We provide a pathwise construction of the collection $(B_n(m))_{1\leq m\leq n}$ and prove that… Expand

## Fractionally integrated inverse stable subordinators

- A. Iksanov, Z. Kabluchko, A. Marynych, G. Shevchenko
- Mathematics
- 24 February 2016

## Limit theorems for the number of occupied boxes in the Bernoulli sieve

- A. Gnedin, A. Iksanov, A. Marynych
- Mathematics
- 27 January 2010

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