Matas Šileikis

activity

20162021

collaborators

6 papers

cs.CG2021

Non-homotopic Loops with a Bounded Number of Pairwise Intersections

Václav Blažej, Michal Opler, Matas Šileikis +1

Let $V_{n}$ be a set of $n$ points in the plane and let $x \in / V_{n}$ . An $x$ -loop is a continuous closed curve not containing any point of $V_{n}$ . We say that two $x$ -loops are non-…

math.CO2020

Sandwiching biregular random graphs

Tereza Klimošová, Christian Reiher, Andrzej Ruciński +1

Let $G (n, n, m)$ be a uniformly random $m$ -edge subgraph of the complete bipartite graph $K_{n, n}$ with bipartition $(V_{1}, V_{2})$ , where $n_{i} = ∣ V_{i} ∣$ . Given a real number $p \in [0,1…

math.PR2019

Upper tail bounds for Stars

Matas Šileikis, Lutz Warnke

For r \ge 2, let X be the number of r-armed stars K_{1,r} in the binomial random graph G_{n,p}. We study the upper tail \Pr(X \ge (1+ε)\E X), and establish exponential bounds which…

math.CO2018

A central limit theorem for almost local additive tree functionals

Dimbinaina Ralaivaosaona, Matas Šileikis, Stephan Wagner

An additive functional of a rooted tree is a functional that can be calculated recursively as the sum of the values of the functional over the branches, plus a certain toll functio…

math.PR2018

A counterexample to the DeMarco-Kahn Upper Tail Conjecture

Matas Šileikis, Lutz Warnke

Given a fixed graph H, what is the (exponentially small) probability that the number X_H of copies of H in the binomial random graph G_{n,p} is at least twice its mean? Studied int…

math.PR2016

Multivariate normal limit laws for the numbers of fringe subtrees in $m$ -ary search trees and preferential attachment trees

Cecilia Holmgren, Svante Janson, Matas Šileikis

We study fringe subtrees of random $m$ -ary search trees and of preferential attachment trees, by putting them in the context of generalised Pólya urns. In particular we show that…