Titlebook: Geometric Aspects of Functional Analysis; Israel Seminar (GAFA Bo‘az Klartag,Emanuel Milman Book 2020 Springer Nature Switzerland AG 2020 A

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A Generalized Central Limit Conjecture for Convex Bodies,t (up to a small factor) to the KLS conjecture. Any polynomial improvement in the current KLS bound of .. in . implies the generalized CLT, and vice versa. This tight connection suggests that the generalized CLT might provide insight into basic open questions in asymptotic convex geometry.

BALK

,Further Investigations of Rényi Entropy Power Inequalities and an Entropic Characterization of s-Corated result of Barron (Ann Probab 14:336–342, 1986). Additionally, we give an entropic characterization of the class of .-concave densities, which extends a classical result of Cover and Zhang (IEEE Trans Inform Theory 40(4):1244–1246, 1994).

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MAPLE

小丑

Small Ball Probability for the Condition Number of Random Matrices,mbination of known results and techniques, it was not noticed in the literature before. As a key step of the proof, we apply estimates for the singular values of ., . obtained (under some additional assumptions) by Nguyen.

Crohns-disease

CRATE

Distributed Autonomous Robotic System 6A classical theorem of Alon and Milman states that any . dimensional centrally symmetric convex body has a projection of dimension . which is either close to the .-dimensional Euclidean ball or to the .-dimensional cross-polytope. We extended this result to non-symmetric convex bodies.

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