2 citations · 2 across the 13 of their papers we have counts for
4 papers · 1 filter
Measurable one-ended spanning trees
Matt Bowen, António Girão, Héctor Jardón-Sánchez +1
We show that a one-ended, locally finite, measurable graph on a standard probability space admits a measurable one-ended spanning subtree if and only if it is measure-hyperfinite.…
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…
The ineffectiveness of the regularity lemma for bounded degree graphs
Clark Lyons, Grigory Terlov, Zoltán Vidnyánszky
We show that for any , there is no bound computable from on the size of a graph required to approximate a graph of maximum degree at most up to $\va…
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…