26 citations · 94 across the 17 of their papers we have counts for
18 papers
Hyper-hyperfiniteness and complexity
Joshua Frisch, Forte Shinko, Zoltan Vidnyanszky
We show that if there exists a countable Borel equivalence relation which is hyper-hyperfinite but not hyperfinite, then the complexity of hyperfinite countable Borel equivalence r…
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-…
Minimal subdynamics and minimal flows without characteristic measures
Joshua Frisch, Brandon Seward, Andy Zucker
Given a countable group and a -flow , a measure is called characteristic if it is -invariant. Frisch and Tamuz asked about the existence o…
Realizations of countable Borel equivalence relations
Joshua Frisch, Alexander Kechris, Forte Shinko +1
We study topological realizations of countable Borel equivalence relations, including realizations by continuous actions of countable groups, with additional desirable properties.…
Lifts of Borel actions on quotient spaces
Joshua Frisch, Alexander Kechris, Forte Shinko
Given a countable Borel equivalence relation E and a countable group G, we study the problem of when a Borel action of G on X/E can be lifted to a Borel action of G on X.
A dichotomy for Polish modules
Joshua Frisch, Forte Shinko
Let be a ring equipped with a proper norm. We show that under suitable conditions on , there is a natural basis under continuous linear injection for the set of Polish -m…
Quasi-Regular Sequences
Joshua Frisch, Wade Hann-Caruthers, Pooya Vahidi Ferdowsi
Let be a countable alphabet. For , an infinite sequence with characters from is called -quasi-regular, if for each the ratio of the longest to short…
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…
Characteristic measures of symbolic dynamical systems
Joshua Frisch, Omer Tamuz
A probability measure is a characteristic measure of a topological dynamical system if it is invariant to the automorphism group of the system. We show that zero entropy shifts alw…
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…
Measurable Riemannian structure on higher dimensional harmonic Sierpinski gaskets
Sara Chari, Joshua Frisch, Daniel J. Kelleher +1
We prove existence of a measurable Riemannian structure on higher-dimensional harmonic Sierpinski gasket fractals and deduce Gaussian heat kernel bounds in the geodesic metric. Our…
Normal amenable subgroups of the automorphism group of the full shift
Joshua Frisch, Tomer Schlank, Omer Tamuz
We show that every normal amenable subgroup of the automorphism group of the full shift is contained in its center. This follows from the analysis of this group's Furstenberg topol…
Symbolic dynamics on amenable groups: the entropy of generic shifts
Joshua Frisch, Omer Tamuz
Let be a finitely generated amenable group. We study the space of shifts on over a given finite alphabet . We show that the zero entropy shifts are generic in this space…
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.