4 papers
Point processes, cost, and the growth of rank in locally compact groups
Miklós Abért, Sam Mellick
Let be a locally compact, second countable, unimodular group that is nondiscrete and noncompact. We explore the theory of invariant point processes on . We show that every f…
Uniform rank gradient, cost and local-global convergence
Miklós Abért, László Márton Tóth
We analyze the rank gradient of finitely generated groups with respect to sequences of subgroups of finite index that do not necessarily form a chain, by connecting it to the cost…
Matchings in Benjamini-Schramm convergent graph sequences
Miklos Abért, Péter Csikvári, Péter Frenkel +1
We introduce the matching measure of a finite graph as the uniform distribution on the roots of the matching polynomial of the graph. We analyze the asymptotic behavior of the matc…
Dynamical properties of profinite actions
Miklós Abért, Gábor Elek
We study profinite actions of residually finite groups in terms of weak containment. We show that two strongly ergodic profinite actions of a group are weakly equivalent if and onl…