26 citations · 94 across the 17 of their papers we have counts for
8 papers · 1 filter
Poisson Boundary for Upper-Triangular Groups
Anna Erschler, Josh Frisch, Mark Rychnovsky
We prove that finite entropy random walks on the torsion-free Baumslag group in dimension have non-trivial Poisson boundary. This is in contrast with the torsion case where t…
The Poisson boundary of hyperbolic groups without moment conditions
Kunal Chawla, Behrang Forghani, Joshua Frisch +1
We prove that the Poisson boundary of a random walk with finite entropy on a non-elementary hyperbolic group can be identified with its hyperbolic boundary, without assuming any mo…
Poisson boundary of group extensions
Anna Erschler, Joshua Frisch
Given a finitely generated group, the well-known Stability Problem asks whether the non-triviality of the Poisson-Furstenberg boundary (which is equivalent to the existence of non-…
Quotients by countable subgroups are hyperfinite
Joshua Frisch, Forte Shinko
We show that for any Polish group and any countable normal subgroup , the coset equivalence relation is a hyperfinite Borel equivalence relation. In par…
Non-virtually nilpotent groups have infinite conjugacy class quotients
Joshua Frisch, Pooya Vahidi Ferdowsi
We offer in this note a self-contained proof of the fact that a finitely generated group is not virtually nilpotent if and only if it has a quotient with the infinite conjugacy cla…
Choquet-Deny groups and the infinite conjugacy class property
Joshua Frisch, Yair Hartman, Omer Tamuz +1
A countable discrete group is called Choquet-Deny if for every non-degenerate probability measure on it holds that all bounded -harmonic functions are constant. We s…
Strong amenability and the infinite conjugacy class property
Joshua Frisch, Omer Tamuz, Pooya Vahidi Ferdowsi
A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if i…
Transitive graphs uniquely determined by their local structure
Joshua Frisch, Omer Tamuz
We show that the "grandfather graph" has the following property: it is the unique completion to a transitive graph of a large enough finite subgraph of itself.