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math.PR2026
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…
math.PR2025
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…
math.PR2025
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…