29 citations · 67 across the 12 of their papers we have counts for
14 papers
On the structure of graph product von Neumann algebras
Ian Charlesworth, Rolando de Santiago, Ben Hayes +3
We undertake a comprehensive study of structural properties of graph products of von Neumann algebras equipped with faithful, normal states, as well as properties of the graph prod…
Random permutation matrix models for graph products
Ian Charlesworth, Rolando de Santiago, Ben Hayes +3
Graph independence (also known as -independence or -independence) is a mixture of classical independence and free independence corresponding to graph products or groups and o…
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…
On Free Stein Dimension
Ian Charlesworth, Brent Nelson
We establish several properties of the free Stein dimension, an invariant for finitely generated unital tracial -algebras. We give formulas for its behaviour under direct sums a…
Distortion for multifactor bimodules and representations of multifusion categories
Marcel Bischoff, Ian Charlesworth, Samuel Evington +2
We call a von Neumann algebra with finite dimensional center a multifactor. We introduce an invariant of bimodules over multifactors that we call modular distortion, and…
Matrix models for -free independence
Ian Charlesworth, Benoît Collins
We investigate tensor products of random matrices, and show that independence of entries leads asymptotically to -free independence, a mixture of classical and free in…
Analogues of Entropy in Bi-Free Probability Theory: Microstates
Ian Charlesworth, Paul Skoufranis
In this paper, we extend the notion of microstate free entropy to the bi-free setting. In particular, using the bi-free analogue of random matrices, microstate bi-free entropy is d…
Analogues of Entropy in Bi-Free Probability Theory: Non-Microstate
Ian Charlesworth, Paul Skoufranis
In this paper, we extend the notion of non-microstate free entropy to the bi-free setting. Using a diagrammatic approach involving bi-non-crossing diagrams, bi-free difference quot…
Free Stein Irregularity and Dimension
Ian Charlesworth, Brent Nelson
We introduce a free probabilistic quantity called free Stein irregularity, which is defined in terms of free Stein discrepancies. It turns out that this quantity is related via a s…
Simultaneous upper triangular forms for commuting operators in a finite von Neumann algebra
Ian Charlesworth, Ken Dykema, Fedor Sukochev +1
The joint Brown measure and joint Haagerup--Schultz projections for tuples of commuting operators in a von Neumann algebra equipped with a faithful tracial state are investigated,…
An alternating moment condition for bi-freeness
Ian Charlesworth
In this note we demonstrate an equivalent condition for bi-freeness, inspired by the well-known "vanishing of alternating centred moments" condition from free probability. We show…
Combinatorics of Bi-Freeness with Amalgamation
Ian Charlesworth, Brent Nelson, Paul Skoufranis
In this paper, we develop the theory of bi-freeness in an amalgamated setting. We construct the operator-valued bi-free cumulant functions, and show that the vanishing of mixed cum…
Regularity of Polynomials in Free Variables
I. Charlesworth, D. Shlyakhtenko
We show that the spectral measure of any non-commutative polynomial of a non-commutative -tuple cannot have atoms if the free entropy dimension of that -tuple is (see als…
On two-faced families of non-commutative random variables
Ian Charlesworth, Brent Nelson, Paul Skoufranis
We demonstrate that the notions of bi-free independence and combinatorial-bi-free independence of two-faced families are equivalent using a diagrammatic view of bi-non-crossing par…