4 citations · 9 across the 10 of their papers we have counts for
19 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…
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…
Computable Gelfand Duality
Peter Burton, Christopher J. Eagle, Alec Fox +5
We establish a computable version of Gelfand Duality. Under this computable duality, computably compact presentations of metrizable spaces uniformly effectively correspond to compu…
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…
Hyperlinear approximations to amenable groups come from sofic approximations
Peter Burton, Maksym Chaudkhari, Kate Juschenko +1
We provide a quantitative formulation of the equivalence between hyperlinearity and soficity for amenable groups, effectively showing how every hyperlinear approximation to such a…
Hyperlinear approximations to amenable groups come from sofic approximations
Peter Burton
We provide a quantitative formulation of the equivalence between hyperlinearity and soficity for amenable groups, showing that every hyperlinear approximation to such a group is es…
Existence of a zero-free strip for the Riemann zeta function
Peter Burton
In a recent article a breakthrough was made in quantum computer science which established the existence of a phenomenon commonly known as . We show…
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…
Extension of positive definite functions and Connes' embedding conjecture
Peter Burton, Kate Juschenko
In this paper we formulate a conjecture which is a strengthening of an extension theorem of Bakonyi and Timotin for positive definite functions on the free group on two generators.…
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…
A quotient-like construction involving elementary submodels
Peter Burton
This article is an investigation of a method of deriving a topology from a space and an elementary submodel containing it. We first define and give the basic properties of this con…
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…