40 citations · 95 across the 19 of their papers we have counts for
27 papers
Rudolph-Johnson without dynamics: endomorphic rigidity on the circle
Peter Burton, Kate Juschenko
We prove that entropy alone, with no invariance hypothesis, forces a Borel probability measure on the circle toward Lebesgue measure under every sublacunary set of multiplicative e…
Entropic rates from eigenfunction structure for
Peter Burton, Kate Juschenko
In a companion article \cite{RJnodyn} the present authors proved a form of the Rudolph--Johnson theorem which is effective at finite resolution, bounding the low-frequency Fourier…
The zero divisor conjecture and Mealy automata
Ievgen Bondarenko, Kate Juschenko
The zero divisor conjecture is sufficient to prove for certain class of finitely presented groups where the relations are given by a pairing of generators. We associate Mealy autom…
Amenable equivalence relations, Kesten's property, and measurable lamplighters
Maksym Chaudkhari, Kate Juschenko, Friedrich Martin Schneider
We prove a characterization of the amenability of countable Borel equivalence relations in terms of the uniform Liouville property for group actions on their classes. Furthermore,…
Skew-amenability of topological groups
Kate Juschenko, Friedrich Martin Schneider
We study skew-amenable topological groups, i.e., those admitting a left-invariant mean on the space of bounded real-valued functions left-uniformly continuous in the sense of Bourb…
The extension problem in free harmonic analysis
Peter Burton, Kate Juschenko
This paper studies certain aspects of harmonic analysis on nonabelian free groups. We focus on the concept of a positive definite function on the free group and our primary goal is…