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• W3048162826 abstract "Abstract Let $(X_1,dots ,X_m)$ be self-adjoint noncommutative random variables distributed according to the free Gibbs law given by a sufficiently regular convex and semi-concave potential $V$, and let $(S_1,dots ,S_m)$ be a free semicircular family. For $k &lt; m$, we show that conditional expectations and conditional non-microstates free entropy given $X_1$, …, $X_k$ arise as the large $N$ limit of the corresponding conditional expectations and entropy for the $N times N$ random matrix models associated to $V$. Then, by studying conditional transport of measure for the matrix models, we construct an isomorphism $mathrm{W}^*(X_1,dots ,X_m) to mathrm{W}^*(S_1,dots ,S_m)$ that maps $mathrm{W}^*(X_1,dots ,X_k)$ to $mathrm{W}^*(S_1,dots ,S_k)$ for each $k = 1, dots , m$ and that also witnesses the Talagrand inequality for the law of $(X_1,dots ,X_m)$ relative to the law of $(S_1,dots ,S_m)$." @default.
• W3048162826 created "2020-08-13" @default.
• W3048162826 creator A5058529112 @default.
• W3048162826 date "2020-08-06" @default.
• W3048162826 modified "2023-09-24" @default.
• W3048162826 title "Conditional Expectation, Entropy, and Transport for Convex Gibbs Laws in Free Probability" @default.
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• W3048162826 doi "https://doi.org/10.1093/imrn/rnaa181" @default.
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