Zobrazeno 1 - 10
of 68
pro vyhledávání: '"Kolesnik, Brett"'
We give a short proof of a recent result of Claesson, Dukes, Frankl\'in and Stef\'ansson, that connects tournament score sequences and the Erd\H{o}s-Ginzburg-Ziv numbers from additive number theory. We show that this connection is, in fact, an instan
Externí odkaz:
http://arxiv.org/abs/2407.01441
A sequence $d_1\le\cdots\le d_n$ is graphical if it is the degree sequence of a graph. Balister, the second author, Groenland, Johnston and Scott showed that there are asymptotically $C4^n/n^{3/4}$ such sequences. However, the constant $C$ involves a
Externí odkaz:
http://arxiv.org/abs/2406.05110
Autor:
Archer, Eleanor, Hartarsky, Ivailo, Kolesnik, Brett, Olesker-Taylor, Sam, Schapira, Bruno, Valesin, Daniel
In Catalan percolation, all nearest-neighbor edges $\{i,i+1\}$ along $\mathbb Z$ are initially occupied, and all other edges are open independently with probability $p$. Open edges $\{i,j\}$ are occupied if some pair of edges $\{i,k\}$ and $\{k,j\}$,
Externí odkaz:
http://arxiv.org/abs/2404.19583
Autor:
Kolesnik, Brett
The critical beta-splitting tree, introduced by Aldous, is a Markov branching phylogenetic tree of poly-logarithmic height. Recently, by a technical analysis, Aldous and Pittel proved, amongst other results, a central limit theorem for the height $H_
Externí odkaz:
http://arxiv.org/abs/2404.16021
Autor:
Donderwinkel, Serte, Kolesnik, Brett
We study a class of random polymers, introduced by Sina\u{i}, which are related to persistence probabilities in integrated simple random walk bridges. We find the precise asymptotics of these probabilities, and describe their combinatorics, using lim
Externí odkaz:
http://arxiv.org/abs/2403.12941
Autor:
Donderwinkel, Serte, Kolesnik, Brett
We study the relationship between tournaments and random walks. This connection was first observed by Erd\H{o}s and Moser. Winston and Kleitman came close to showing that $S_n=\Theta(4^n/n^{5/2})$. Building on this, and works by Tak\'acs, these asymp
Externí odkaz:
http://arxiv.org/abs/2403.12940
A tournament is an orientation of a graph. Vertices are players and edges are games, directed away from the winner. Kannan, Tetali and Vempala and McShine showed that tournaments with given score sequence can be rapidly sampled, via simple random wal
Externí odkaz:
http://arxiv.org/abs/2401.17210
Brualdi and Li introduced tournament interchange graphs. In such a graph, each vertex represents a tournament. Traversing an edge corresponds to reversing a cyclically directed triangle. Such a triangle is neutral, in that its reversal does not affec
Externí odkaz:
http://arxiv.org/abs/2312.04532
We study an interacting system of competing particles on the real line. Two populations of positive and negative particles evolve according to branching Brownian motion. When opposing particles meet, their charges neutralize and the particles annihil
Externí odkaz:
http://arxiv.org/abs/2312.03669
In $H$-percolation, we start with an Erd\H{o}s--R\'enyi graph ${\mathcal G}_{n,p}$ and then iteratively add edges that complete copies of $H$. The process percolates if all edges missing from ${\mathcal G}_{n,p}$ are eventually added. We find the cri
Externí odkaz:
http://arxiv.org/abs/2312.03663