Morse subgroups and boundaries of random right-angled Coxeter groups

Susse, Tim

doi:10.1007/s10711-022-00747-x

Cited by 1 publication

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“…More recently, Susse [34] studied Morse subgroups and Morse boundaries of random RACG. In forthcoming work [2], the authors of the present paper establish a threshold for connectivity of the square graph of a random graph, a result that settles a conjecture of Susse and has geometric applications to the study of cubical coarse rigidity in random RACG.…”

Section: Related Resultsmentioning

confidence: 99%

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

Behrstock

Falgas–Ravry

Susse

2021

Random Struct Algorithms

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Given a graph Γ, its auxiliary square‐graph □(Γ) is the graph whose vertices are the non‐edges of Γ and whose edges are the pairs of non‐edges which induce a square (i.e., a 4‐cycle) in Γ. We determine the threshold edge‐probability p=pc(n) at which the Erdős–Rényi random graph Γ=Γn,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 Γn,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 WΓn,p a.a.s. becomes strongly algebraically thick of order 1 and has quadratic divergence.

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Section: Related Resultsmentioning

confidence: 99%