David Jekel

On counterexamples to the unification of free entropy

David Jekel

It has been a long-standing open problem to determine when two versions of Voiculescu's free entropy, $χ$ and $χ^{*}$ , agree. OpenAI recently generated the first example with $-\inft…

Simplicity of q-Gaussian C*-algebras

Tattwamasi Amrutam, David Jekel, Mateusz Wasilewski

We show that q-Gaussian $C^{*}$ -algebras for $q \in (- 1, 1)$ have the Dixmier averaging property, and hence are simple with a unique trace. We argue by combining rapid decay and spec…

Questions on the structure of random embeddings of $L (F_{2})$

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…

Exotic full factors via weakly coarse bimodules

David Gao, David Jekel, Srivatsav Kunnawalkam Elayavalli +1

We are able to explicitly compute the bimodule structure of von Neumann algebra inclusions in handle constructions, which arise as inductive limits of iterated amalgamated free pro…

Elementary embeddings into ultrapower $II_{1}$ factors without a UCP lift

David Gao, David Jekel

We show that there are $II_{1}$ factors $M$ and elementary embeddings $M \to M^{U}$ which do not lift to sequences of UCP maps, and in fact $M$ can be chosen from…

The unitary group of a $II_{1}$ factor is SOT-contractible

David Jekel

We show that the unitary group of any SOT-separable $II_{1}$ factor $M$ , with the strong operator topology, is contractible. Combined with several old results, this implies…

Strong convergence to operator-valued semicirculars

David Jekel, Yoonkyeong Lee, Brent Nelson +1

We establish a framework for weak and strong convergence of matrix models to operator-valued semicircular systems parametrized by operator-valued covariance matrices $η= (η_{i,j})_…

The atoms of graph product von Neumann algebras

Ian Charlesworth, David Jekel

We completely classify the atomic summands in a graph product $(M, φ) = *_{v \in G} (M_{v}, φ_{v})$ of von Neumann algebras with faithful normal states. Each type I factor summ…

Operator models and analytic subordination for operator-valued free convolution powers

Ian Charlesworth, David Jekel

We revisit the theory of operator-valued free convolution powers given by a completely positive map $η$ . We first give a general result, with a new analytic proof, that the $η$ -con…

Information geometry for types in the large- $n$ limit of random matrices

David Jekel

We study the interaction between entropy and Wasserstein distance in free probability theory. In particular, we give lower bounds for several versions of free entropy dimension alo…

General solidity phenomena and anticoarse spaces for type $III_{1}$ factors

Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli +1

By developing a theory of anticoarse spaces in the purely infinite setting and using 1-bounded entropy techniques along with recent strong convergence results in random matrix theo…

math.OA2024★ 1 cited

Elementary equivalence and disintegration of tracial von Neumann algebras

David Gao, David Jekel

We prove an analog of the disintegration theorem for tracial von Neumann algebras in the setting of elementary equivalence rather than isomorphism, showing that elementary equivale…

math.PR2024

General limit theorems for mixtures of free, monotone, and boolean independence

David Jekel, Lahcen Oussi, Janusz Wysoczański

We study mixtures of free, monotone, and Boolean independence described by a directed graph $G = (V, E)$ in the context of $T$ -free convolutions of Jekel and Liu. We prove…

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…

Upgraded free independence phenomena for random unitaries

David Jekel, Srivatsav Kunnawalkam Elayavalli

We study upgraded free independence phenomena for unitary elements $u_{1}$ , $u_{2}$ , \dots representing the large- $n$ limit of Haar random unitaries, showing that free independence ext…

Random permutation matrix models for graph products

Ian Charlesworth, Rolando de Santiago, Ben Hayes +3

Graph independence (also known as $ε$ -independence or $λ$ -independence) is a mixture of classical independence and free independence corresponding to graph products or groups and o…

math.OA2023★ 1 cited

Quantum Expanders and Quantifier Reduction for Tracial von Neumann Algebras

Ilijas Farah, David Jekel, Jennifer Pi

We provide a complete characterization of theories of tracial von Neumann algebras that admit quantifier elimination. We also show that the theory of a separable tracial von Neuman…

math.OA2023★ 3 cited

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…

Optimal transport for types and convex analysis for definable predicates in tracial $W^{*}$ -algebras

David Jekel

We investigate the connections between continuous model theory, free probability, and optimal transport/convex analysis in the context of tracial von Neumann algebras. In particula…

Strong 1-boundedness, $L^{2}$ -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…

An Elementary Proof of the Inequality $χ \leq χ^{*}$ for Conditional Free Entropy

David Jekel, Jennifer Pi

Through the study of large deviations theory for matrix Brownian motion, Biane-Capitaine-Guionnet proved the inequality $χ (X) \leq χ^{*} (X)$ that relates two analogs of entropy in fr…