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arXiv · 2306.12763

Noncommutative Poisson boundaries, ultraproducts and entropy

Shuoxing Zhou
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Abstract

We construct the noncommutative Poisson boundaries of tracial von Neumann algebras through the ultraproducts of von Neumann algebras. As an application of this result, we complete the proof of Kaimanovich-Vershik's fundamental theorems regarding noncommutative entropy. We also prove the Amenability-Trivial Boundary equivalence and Choquet-Deny-Type I equivalence for tracial von Neumann algebras.

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Shuoxing Zhou. 2023-06-22. Noncommutative Poisson boundaries, ultraproducts and entropy. https://doi.org/10.1093/imrn%2Frnae022

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