D. Shlyakhtenko

activity

19982026

most citedGrothendieck's Theorem for Operator Spaces

99 citations · 460 across the 54 of their papers we have counts for

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48 papers · 1 filter

math.OA2026

Failure of Strong Convergence of Matrices with Fermionic Entries

Dimitri Shlyakhtenko

Let $Q_{N}^{(k)}$ be an $N \times N$ matrices with entries satisfying CAR, normalized to have variance $1/ N$ with respect to the trace of the CAR algebra. We show that, althoug…

math.OA2026

A Free Analog of Bobkov's Gaussian Isoperimetry Inequality

Dimitri Shlyakhtenko

We prove a one-variable functional inequality which is the free probability analog of Bobkov's isoperimetry inequality. The inequality involves the $L^{1}$ norm of the difference quo…

math.OA2025

Establishing strong 1-boundedness via non-microstates free entropy techniques

Benjamin Major, Dimitri Shlyakhtenko

We show that, for many choices of finite tuples of generators $X = (x_{1}, \dots, x_{d})$ of a tracial von Neumann algebra $(M, τ)$ satisfying certain decomposition properties (non-pr…

math.OA2022

A Inequality for Non-Microstates Free Entropy Dimension for Crossed Products by Finite Abelian Groups

D. Shlyakhtenko

For certain generating sets of the subfactor pair $M \subset M ⋊ G$ where $G$ is a finite abelian group we prove an approximate inequality between their non-microstates free en…

math.OA2021★ 12 cited

Duality for optimal couplings in free probability

Wilfrid Gangbo, David Jekel, Kyeongsik Nam +1

We study the free probabilistic analog of optimal couplings for the quadratic cost, where classical probability spaces are replaced by tracial von Neumann algebras, and probability…

math.OA2021

Tracial smooth functions of non-commuting variables and the free Wasserstein manifold

David Jekel, Wuchen Li, Dimitri Shlyakhtenko

We formulate a free probabilistic analog of the Wasserstein manifold on $R^{d}$ (the formal Riemannian manifold of smooth probability densities on $R^{d}$ ), and we us…