Titlebook: Geometric Aspects of Functional Analysis; Israel Seminar 2006– Bo‘az Klartag,Shahar Mendelson,Vitali D. Milman Book 2012 Springer-Verlag Be

Largess

Tightness of Fluctuations of First Passage Percolation on Some Large Graphs,he binary tree, from the root to a boundary of a ball, is generalized to a class of graphs which includes all lattices in hyperbolic spaces and the lamplighter graph over .. This class of graphs is closed under product with any bounded degree graph. Few open problems and conjectures are gathered at

有斑点

Intercept

A Family of Unitary Operators Satisfying a Poisson-Type Summation Formula,unitary Fourier–Poisson operator which satisfies this formula. We next find the diagonal form of this operator, and prove that under weaker conditions on the weights, a unique unitary operator still exists which satisfies a Poisson summation formula in operator form. We also generalize the interplay

Dictation

减至最低

,On the Distribution of the ψ2-Norm of Linear Functionals on Isotropic Convex Bodies,of the body ..(.) with support function .. The approach in all the related works does not provide estimates on the measure of directions satisfying a ψ.-estimate with a given constant .. We introduce the function . and we discuss lower bounds for ψ.(.), .. Information on the distribution of the ψ.-n

–DOX

A Remark on Vertex Index of the Convex Bodies,ere given in the general case as well as for some basic examples. In this note we improve these bounds and discuss their sharpness. We show that .which is asymptotically sharp. We also show that the estimate .obtained in [Bezdek, Litvak, Adv. Math. ., 626–641 (2007)] (here ovr(.) denotes the outer v

松鸡

Inner Regularization of Log-Concave Measures and Small-Ball Estimates,ginals. To this end, a standard preprocessing step is to convolve with a Gaussian measure, but this has the disadvantage of destroying small-ball information. We propose an alternative preprocessing step for making the measure seem super-Gaussian, at least up to reasonably high moments, which does n

松软无力

An Operator Equation Generalizing the Leibniz Rule for the Second Derivative, mild regularity and non-degeneracy assumption on ., we show that the operators . and . have to be of a very restricted type. In addition to the operator solutions . of the Leibniz rule derivation equation corresponding to . = 0, .which are of the form .. and . may be of the following three types .f

Indolent

Projections of Probability Distributions: A Measure-Theoretic Dvoretzky Theorem,er mild conditions, most one-dimensional marginals are approximately Gaussian if . is large. In earlier work, the author used entropy techniques and Stein’s method to show that this phenomenon persists in the bounded-Lipschitz distance for .-dimensional marginals of .-dimensional distributions, if .