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math.OA2026
On the Isomorphism of Semicircular Algebras
D. Shlyakhtenko
Building on OpenAI's proof of isomorphism of free group factors, we give a self-contained proof of a corresponding result for -algebras generated by free semicircular system…
math.OA2026
On the II Factors of Fuchsian Groups
D. Shlyakhtenko
We show that von Neumann algebras of fundamental groups of closed orientable surfaces of genus are free group factors on generators. The key technical ingredient inv…
math.OA2016
Free transport for convex potentials
Y. Dabrowski, A. Guionnet, D. Shlyakhtenko
We construct non-commutative analogs of transport maps among free Gibbs state satisfying a certain convexity condition. Unlike previous constructions, our approach is non-perturbat…