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Title: Square percolation and the threshold for quadratic divergence in random right‐angled Coxeter groups
Abstract

Given a graph, its auxiliarysquare‐graphis the graph whose vertices are the non‐edges ofand whose edges are the pairs of non‐edges which induce a square (i.e., a 4‐cycle) in. We determine the threshold edge‐probabilityat which the Erdős–Rényi random graphbegins to asymptotically almost surely (a.a.s.) have a square‐graph with a connected component whose squares together cover all the vertices of. We show, a polylogarithmic improvement on earlier bounds ondue to Hagen and the authors. As a corollary, we determine the thresholdat which the random right‐angled Coxeter groupa.a.s. becomes strongly algebraically thick of order 1 and has quadratic divergence.

 
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NSF-PAR ID:
10367039
Author(s) / Creator(s):
 ;  ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Random Structures & Algorithms
Volume:
60
Issue:
4
ISSN:
1042-9832
Page Range / eLocation ID:
p. 594-630
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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