4 citations · 9 across the 10 of their papers we have counts for
12 papers · 1 filter
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…
Formulations of Furstenberg's conjecture in complex analysis and operator algebras
Peter Burton, Jane Panangaden
Furstenberg's conjecture has remained a central open problem in ergodic theory for over years, and it serves as the basic test case for a broad class of ri…
Synergodic actions of product groups
Peter Burton
This article studies a structural aspect of measure-preserving actions of products of countable discrete groups, involving a so-called 'synergodic decomposition' in terms of the er…
Weak containment of measure preserving group actions
Peter Burton, Alexander S. Kechris
We survey recent progress in the theory of weak containment of measure preserving group actions.
Invariant random subgroups and action versus representation maximality
Peter J. Burton, Alexander S. Kechris
We show that weak containment of free ergodic measure-preserving actions of is not equivalent to weak containment of the corresponding Koopman representations.…
Uniform mixing and completely positive sofic entropy
Tim Austin, Peter Burton
Let be a countable discrete sofic group. We define a concept of uniform mixing for measure-preserving -actions and show that it implies completely positive sofic entropy. Wh…
Weak equivalence of stationary actions and the entropy realization problem
Peter Burton, Martino Lupini, Omer Tamuz
We introduce the notion of weak containment for stationary actions of a countable group and define a natural topology on the space of weak equivalence classes. We prove that Furste…
Completely positive entropy actions of sofic groups with in their center
Peter Burton
Let be a sofic group with a copy of in its center. We construct an uncountable family of pairwise nonisomorphic measure-preserving actions with completely posi…
Naive entropy of dynamical systems
Peter Burton
We study an invariant of dynamical systems called naive entropy, which is defined for both measurable and topological actions of any countable group. We focus on nonamenable groups…
A topological semigroup structure on the space of actions modulo weak equivalence
Peter Burton
We introduce a topology on the space of actions modulo weak equivalence finer than the one previously studied in the literature. We show that the product of actions is a continuous…
Topology and convexity in the space of actions modulo weak equivalence
Peter Burton
We analyse the structure of the quotient of the space of measure-preserving actions of a countable discrete group by the relation of weak equivalence. This…