40 citations · 130 across the 31 of their papers we have counts for
32 papers
Questions on the structure of random embeddings of
Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli
Motivated by recent developments at the interface of operator algebras and random matrix theory, we propose new conjectures concerning the asymptotic structure of random matrix mod…
Coamenability and strong ergodicity
Ben Hayes
Following methods of Bannon-Marrakchi-Ozawa, we show that for coamenable inclusion of ergodic, probability measure-preserving relations, we have that…
Strongly 1-bounded inner amenable groups
Ben Hayes, Srivatsav Kunnawalkam Elayavalli
It is shown that finitely presented icc inner amenable groups yield strongly 1-bounded II_1 factors.
Consequences of the random matrix solution to the Peterson-Thom conjecture
Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli
In this paper we show various new structural properties of free group factors using the recent resolution (due independently to Belinschi-Capitaine and Bordenave-Collins) of the Pe…
Approximate homomorphisms and sofic approximations of orbit equivalence relations
Ben Hayes, Srivatsav Kunnawalkam Elayavalli
We show that for every countable group, any sequence of approximate homomorphisms with values in permutations can be realized as the restriction of a sofic approximation of an orbi…
On sofic approximations of non amenable groups
Ben Hayes, Srivatsav Kunnawalkam Elayavalli
In this paper we exhibit for every non amenable group that is initially sub-amenable (sometimes also referred to as LEA), two sofic approximations that are not conjugate by any aut…
Strong 1-boundedness, -Betti numbers, algebraic soficity, and graph products
Ian Charlesworth, Rolando de Santiago, Ben Hayes +3
We show that graph products of non trivial finite dimensional von Neumann algebras are strongly 1-bounded when the underlying *-algebra has vanishing first L2-Betti number. The pro…
Vanishing first cohomology and strong 1-boundedness for von Neumann algebras
Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli
In this paper, we obtain a new proof result of Shlyakhtenko which states that if is a sofic, finitely presented group with vanishing first -Betti number, then is…
Property (T) and strong -boundedness for von Neumann algebras
Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli
The notion of strong 1-boundedness for finite von Neumann algebras was introduced by Jung in arXiv:math/0510576 . This framework provided a free probabilistic approach to study rig…
A random matrix approach to the Peterson-Thom conjecture
Ben Hayes
The Peterson-Thom conjecture asserts that any diffuse, amenable subalgebra of a free group factor is contained in a unique maximal amenable subalgebra. This conjecture is motivated…
A multiplicative ergodic theorem for von Neumann algebra valued cocycles
Lewis Bowen, Ben Hayes, Yuqing +1
The classical Multiplicative Ergodic Theorem (MET) of Oseledets is generalized here to cocycles taking values in a semi-finite von Neumann algebra. This allows for a continuous Lya…
A random matrix approach to absorption in free products
Ben Hayes, David Jekel, Brent Nelson +1
This paper gives a free entropy theoretic perspective on amenable absorption results for free products of tracial von Neumann algebras. In particular, we give the first free entrop…
Maximal rigid subalgebras of deformations and -cohomology
Rolando de Santiago, Ben Hayes, Daniel J. Hoff +1
In the past two decades, Sorin Popa's breakthrough deformation/rigidity theory has produced remarkable rigidity results for von Neumann algebras which can be deformed inside a…
Harmonic Models and Bernoullicity
Ben Hayes
We give many examples of algebraic actions which are factors of Bernoulli shifts. These include certain harmonic models over left orderable groups of large enough growth, as well a…
Max-Min theorems for weak containment, square summable homoclinic points, and completely positive entropy
Ben Hayes
We prove a max-min theorem for weak containment in the context of algebraic actions. Namely, we show that given an algebraic action of on there is a maximal, closed -in…
An Operator theoretic approach to the convergence of rearranged Fourier series
Keaton Hamm, Ben Hayes, Armenak Petrosyan
This article studies the rearrangement problem for Fourier series introduced by P.L. Ulyanov, who conjectured that every continuous function on the torus admits a rearrangement of…
Local weak-Convergence, algebraic actions, and a max-min principle
Ben Hayes
We continue our study of when topological and measure-theoretic entropy agree for algebraic action of sofic groups. Specifically, we provide a new abstract method to prove that an…
Weak equivalence to Bernoulli shifts for some algebraic actions
Ben Hayes
Namely, we prove that if is a countable, discrete group and is invertible on but is not invertible in , then the…
Metric Approximations of Wreath Products
Ben Hayes, Andrew Sale
Given the large class of groups already known to be sofic, there is seemingly a shortfall in results concerning their permanence properties. We address this problem for wreath prod…
Relative entropy and the Pinsker product formula for sofic groups
Ben Hayes
We continue our study of the outer Pinsker factor for probability measure-preserving actions of sofic groups. Using the notion of doubly quenched convergence developed by Austin, w…
Local and doubly empirical convergence and the entropy of algebraic actions of sofic Groups
Ben Hayes
Let G be a sofic group and X a compact group that G acts on by automorphisms. Using (and reformulating) the notion of doubly-quenched convergence developed by Austin, we show that…
The Wreath Product of Two Sofic Groups is Sofic
Ben Hayes, Andrew Sale
Given sofic approximations for countable, discrete groups , we construct a sofic approximation for their wreath product .
Mixing and Spectral Gap Relative to Pinsker Factors for Sofic Groups
Ben Hayes
Motivated by our previous results, we investigate structural properties of probability measure-preserving actions of sofic groups relative to their Pinsker factor. We also consider…
Sofic Entropy of Gaussian Actions
Ben Hayes
Associated to any orthogonal representation of a countable discrete group is an probability measure-preserving action called the Gaussian action. Using the Polish model formalism w…