19 citations · 89 across the 12 of their papers we have counts for
5 papers · 1 filter
Concentration inequalities for vector-valued martingales
Tomas Juškevičius, Matas Šileikis
In this paper, we establish several deviation inequalities for the norms of vector-valued martingales, achieving bounds of the same quality as those available in the classical one-…
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…
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…
Multivariate normal limit laws for the numbers of fringe subtrees in -ary search trees and preferential attachment trees
Cecilia Holmgren, Svante Janson, Matas Šileikis
We study fringe subtrees of random -ary search trees and of preferential attachment trees, by putting them in the context of generalised Pólya urns. In particular we show that…
Optimal Probability Inequalities for Random Walks related to Problems in Extremal Combinatorics
Dainius Dzindzalieta, Matas Šileikis, Tomas Juškevičius
Let S_n=X_1+...+X_n be a sum of independent symmetric random variables such that |X_{i}|\leq 1. Denote by W_n=ε_{1}+...+ε_{n} a sum of independent random variables such that \prob{…