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

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,The Lower Bound for Koldobsky’s Slicing Inequality via Random Rounding,and all . . Our bound is optimal, up to the value of the universal constant. It improves slightly upon the results of the first named author and Koldobsky, which included a doubly-logarithmic error. The proof is based on an efficient way of discretizing the unit sphere.

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Two-Sided Estimates for Order Statistics of Log-Concave Random Vectors,uncorrelated coordinates. Our bounds are exact up to multiplicative universal constants in the unconditional case for all . and in the isotropic case for .?≤?.???... We also derive two-sided estimates for expectations of sums of . largest moduli of coordinates for some classes of random vectors.

ABHOR

,Further Investigations of Rényi Entropy Power Inequalities and an Entropic Characterization of s-CoBobkov and Chistyakov (IEEE Trans Inform Theory 61(2):708–714, 2015) fails when the Rényi parameter .?∈?(0, 1), we show that random vectors with .-concave densities do satisfy such a Rényi entropy power inequality. Along the way, we establish the convergence in the Central Limit Theorem for Rényi en

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Concentration of the Intrinsic Volumes of a Convex Body,quence of intrinsic volumes. The main result states that the intrinsic volume sequence concentrates sharply around a specific index, called the central intrinsic volume. Furthermore, among all convex bodies whose central intrinsic volume is fixed, an appropriately scaled cube has the intrinsic volum

土產(chǎn)

Two Remarks on Generalized Entropy Power Inequalities,nicity and entropy comparison of weighted sums of independent identically distributed log-concave random variables. We also present a complex analogue of a recent dependent entropy power inequality of Hao and Jog, and give a very simple proof.

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On the Geometry of Random Polytopes,ric random variable that has variance 1, let Γ?=?(..) be an .?×?. random matrix whose entries are independent copies of ., and set .., …, .. to be the rows of Γ. Then under minimal assumptions on . and as long as .?≥?.., with high probability

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