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math.PR2025
Heavy repulsion of clusters in Bernoulli percolation
Sasha Bell, Tasmin Chu, Owen Rodgers +2
We study Bernoulli percolation on (non)unimodular quasi-transitive graphs and prove that, almost surely, for any two heavy clusters and , the set of vertices in wi…
math.PR2025
Weighted-amenability and percolation
Grigory Terlov, Ádám Timár
In 1999, Benjamini, Lyons, Peres, and Schramm introduced a notion of weighted-amenability for transitive graphs that is equivalent to the amenability of its automorphism group. For…