Titlebook: Geometric Aspects of Functional Analysis; Israel Seminar (GAFA Bo‘az Klartag,Emanuel Milman Book 2017 Springer International Publishing AG

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Concentration Properties of Restricted Measures with Applications to Non-Lipschitz Functions,We show that, for any metric probability space (., ., .) with a subgaussian constant ..(.) and any Borel measurable set . ⊂ ., we have ., where .. is a normalized restriction of . to the set . and . is a universal constant. As a consequence, we deduce concentration inequalities for non-Lipschitz functions.

Obstruction

On Random Walks in Large Compact Lie Groups,Let . be the group .(.) or .(.) with . large. How long does it take for a random walk on . to approximate uniform measure? It is shown that in certain natural examples an .-approximation is achieved in time ..

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BRIDE

Valuations on the Space of Quasi-Concave Functions,We characterize the valuations on the space of quasi-concave functions on ., that are rigid motion invariant and continuous with respect to a suitable topology. Among them we also provide a specific description of those which are additionally monotone.

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Generator

A Remark on Projections of the Rotated Cube to Complex Lines,Motivated by relations with a symplectic invariant known as the “cylindrical symplectic capacity”, in this note we study the expectation of the area of a minimal projection to a complex line for a randomly rotated cube.

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On the Expectation of Operator Norms of Random Matrices,We prove estimates for the expected value of operator norms of Gaussian random matrices with independent (but not necessarily identically distributed) and centered entries, acting as operators from . to ..., 1 ≤ .. ≤ 2 ≤ . < ..

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Free-Radical

,Royen’s Proof of the Gaussian Correlation Inequality,We present in detail Thomas Royen’s proof of the Gaussian correlation inequality which states that .(. ∩ .) ≥ .(.).(.) for any centered Gaussian measure . on . and symmetric convex sets ., . in ..