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Connectivity for square percolation and coarse cubical rigidity in random right-angled Coxeter groups
Jason Behrstock, R. Altar Ciceksiz, Victor Falgas-Ravry
We consider random right-angled Coxeter groups, , whose presentation graph is taken to be an Erdős--Rényi random graph, i.e., . We use techniques…
Bootstrap percolation in random geometric graphs
Victor Falgas-Ravry, Amites Sarkar
Following Bradonjić and Saniee, we study a model of bootstrap percolation on the Gilbert random geometric graph on the -dimensional torus. In this model, the expected number of…
Square percolation and the threshold for quadratic divergence in random right-angled Coxeter groups
Jason Behrstock, Victor Falgas-Ravry, Tim Susse
Given a graph , its auxiliary \emph{square-graph} is the graph whose vertices are the non-edges of and whose edges are the pairs of non-edges which induce a squ…
Long paths and connectivity in {}-independent random graphs
A. Nicholas Day, Victor Falgas-Ravry, Robert Hancock
Given a graph , a probability measure on the subsets of the edge set of is said to be -independent if events determined by edge sets that are at graph distance at lea…