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

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,Shephard’s Inequalities, Hodge-Riemann Relations, and a Conjecture of Fedotov,The classic monograph . by Burago and Zalgaller states a conjecture on the validity of higher-order analogues of Shephard’s inequalities, which is attributed to Fedotov. In this note we disprove Fedotov’s conjecture by showing that it contradicts the Hodge-Riemann relations for simple convex polytop

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Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices,bler (KL) divergence assuming . satisfies a log-Sobolev inequality and the Hessian of . is bounded. Notably, we do not assume convexity or bounds on higher derivatives. We prove convergence guarantees in Rényi divergence of order . assuming the limit of ULA satisfies isoperimetry, namely either the

savage

https://doi.org/10.1007/978-3-319-93272-9 of their present central interests. More precisely, that part of their interests that relates to Asymptotic Geometric Analysis. Many agreed, and I am posting below the short texts I received. After each of them, I will place my comments, as well as some problems that arise when reading these texts.

Salivary-Gland

https://doi.org/10.1007/978-0-230-21399-9competitive ratio . in any normed space, which is . tight for .. In Euclidean space, our algorithm also achieves competitive ratio ., nearly matching a . lower bound when . is subexponential in .. Our approach extends that of Bubeck et al. (Proceedings of the Fourteenth Annual ACM-SIAM Symposium on