Titlebook: Geometric Aspects of Functional Analysis; Israel Seminar (GAFA Ronen Eldan,Bo‘a(chǎn)z Klartag,Emanuel Milman Book 2023 The Editor(s) (if applica

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https://doi.org/10.1057/9781403934314The works of Bennett, Carbery, Christ, Tao and of Valdimarsson have clarified when equality holds in the Brascamp-Lieb inequality. Here we characterize the case of equality in the Geometric case of Barthe’s reverse Brascamp-Lieb inequality.

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Poverty and Slowness of Voluntary Movement,The aim of this note is to show that the local form of the logarithmic Brunn-Minkowski conjecture holds for zonoids. The proof uses a variant of the Bochner method due to Shenfeld and the author.

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On the Gaussian Surface Area of Spectrahedra,We show that for sufficiently large . and . for some universal constant ., a random spectrahedron with matrices drawn from Gaussian orthogonal ensemble has Gaussian surface area . with high probability.

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,The Case of Equality in Geometric Instances of Barthe’s Reverse Brascamp-Lieb Inequality,The works of Bennett, Carbery, Christ, Tao and of Valdimarsson have clarified when equality holds in the Brascamp-Lieb inequality. Here we characterize the case of equality in the Geometric case of Barthe’s reverse Brascamp-Lieb inequality.

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The Entropic Barrier Is ,-Self-Concordant,For any convex body ., S. Bubeck and R. Eldan introduced the entropic barrier on . and showed that it is a .-self-concordant barrier. In this note, we observe that the optimal bound of . on the self-concordance parameter holds as a consequence of the dimensional Brascamp–Lieb inequality.