6 papers
Parabolic-hyperbolic dichotomy through half-plane coexistence
Ádám 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, Ádám 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…
Uniform Borel Amenability
Gábor Elek, Ádám 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…
On invariant generating sets for the cycle space
Ádám Timár
Consider a unimodular random graph, or just a finitely generated Cayley graph. When does its cycle space have an invariant random generating set of cycles such that every edge is c…
Finite-energy infinite clusters without anchored expansion
Gábor Pete, Ádám Timár
Hermon and Hutchcroft have recently proved the long-standing conjecture that in Bernoulli(p) bond percolation on any nonamenable transitive graph G, at any p > p_c(G), the probabil…
The Free Uniform Spanning Forest is disconnected in some virtually free groups, depending on the generator set
Gábor Pete, Ádám Timár
We prove the rather counterintuitive result that there exist finite transitive graphs H and integers k such that the Free Uniform Spanning Forest in the direct product of the k-reg…