Paper Info
Title
Square percolation and the threshold for quadratic divergence in random right-angled Coxeter groups
Abstract
Given a graph Gamma, its auxiliary square-graph (Gamma) is the graph whose vertices are the non-edges of Gamma and whose edges are the pairs of non-edges which induce a square (i.e., a 4-cycle) in Gamma. We determine the threshold edge-probability p=pc(n) at which the Erdos-Renyi random graph Gamma=Gamma n,p begins to asymptotically almost surely (a.a.s.) have a square-graph with a connected component whose squares together cover all the vertices of Gamma n,p. We show pc(n)=6-2/n, a polylogarithmic improvement on earlier bounds on pc(n) due to Hagen and the authors. As a corollary, we determine the threshold p=pc(n) at which the random right-angled Coxeter group W Gamma n,p a.a.s. becomes strongly algebraically thick of order 1 and has quadratic divergence.
Year
DOI
Venue
2022
10.1002/rsa.21049
RANDOM STRUCTURES & ALGORITHMS
Keywords
DocType
Volume
divergence, geometric group theory, random graphs, random groups, right-angled Coxeter groups, square percolation
Journal
60
Issue
ISSN
Citations 
4
1042-9832
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Jason Behrstock100.34
Victor Falgas-Ravry2287.46
Tim Susse300.34