5 papers
Uniform Borel Amenability
Gábor Elek, Ãdám Timár
We study a uniform, quantitative form of the amenability-hyperfiniteness paradigm for bounded-degree Borel graphs generating countable Borel equivalence relations. We introduce \em…
Parabolic-hyperbolic dichotomy through half-plane coexistence
Ãdám Timár
Consider a unimodular random planar map (URM) with an invariant ergodic percolation having infinite primal and dual clusters. We say that there is half-plane coexistence if both th…
Indistinguishability for recurrent clusters
Damis El Alami, Gábor Pete, Ãdám Timár
We introduce a general framework to show the indistinguishability of infinite clusters (ergodicity of the cluster subrelation) in group-invariant percolation processes with a weake…
Strong almost finiteness
Gábor Elek, Ãdám Timár
A countable, bounded degree graph is almost finite if it has a tiling with isomorphic copies of finitely many Følner sets, and we call it strongly almost finite, if the tiling can…
Weighted-amenability and percolation
Grigory Terlov, Ãdám 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…