19 citations · 89 across the 12 of their papers we have counts for
14 papers
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-…
Prominent examples of flip processes
Pedro Araújo, Jan Hladký, Eng Keat Hng +1
Flip processes, introduced in [Garbe, Hladký, Šileikis, Skerman: From flip processes to dynamical systems on graphons], are a class of random graph processes defined using a rule w…
Non-homotopic Loops with a Bounded Number of Pairwise Intersections
Václav Blažej, Michal Opler, Matas Šileikis +1
Let be a set of points in the plane and let . An -loop is a continuous closed curve not containing any point of . We say that two -loops are non-…
Sandwiching biregular random graphs
Tereza Klimošová, Christian Reiher, Andrzej Ruciński +1
Let be a uniformly random -edge subgraph of the complete bipartite graph with bipartition , where . Given a real number $p \in [0,1…
Counting extensions revisited
Matas Šileikis, Lutz Warnke
We consider rooted subgraphs in random graphs, i.e., extension counts such as (i) the number of triangles containing a given vertex or (ii) the number of paths of length three conn…
A limit theorem for small cliques in inhomogeneous random graphs
Jan Hladky, Christos Pelekis, Matas Sileikis
The theory of graphons comes with a natural sampling procedure, which results in an inhomogeneous variant of the Erdős--Rényi random graph, called -random graphs. We prove, via…
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 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…
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…
Embedding the Erdős-Rényi Hypergraph into the Random Regular Hypergraph and Hamiltonicity
Andrzej Dudek, Alan Frieze, Andrzej Ruciński +1
We establish an inclusion relation between two uniform models of random -graphs (for constant ) on labeled vertices: , the random -graph wi…
Loose Hamilton Cycles in Regular Hypergraphs
Andrzej Dudek, Alan Frieze, Andrzej Ruciński +1
We establish a relation between two uniform models of random -graphs (for constant ) on labeled vertices: , the random -graph with exactly edges, and…
Approximate counting of regular hypergraphs
Andrzej Dudek, Alan Frieze, Andrzej Ruciński +1
In this paper we asymptotically count -regular -uniform hypergraphs on vertices, provided is fixed and . In doing so, we extend to hypergraphs a sw…
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{…