Titlebook: Convexity and Concentration; Eric Carlen,Mokshay Madiman,Elisabeth M. Werner Conference proceedings 2017 Springer Science+Business Media L

Spirometry

Concentration of Measure Principle and Entropy-Inequalitiesiew of the links between concentration properties, transport-entropy inequalities, and logarithmic Sobolev inequalities for some specific transport costs. By giving few examples, we emphasize optimal weak transport costs as an efficient tool to establish new transport inequality and new concentratio

NIP

Structured Random Matrices. Much of the literature in this area is concerned with matrices that possess many exact or approximate symmetries, such as matrices with i.i.d. entries, for which precise analytic results and limit theorems are available. Much less well understood are matrices that are endowed with an arbitrary str

新义

Rates of Convergence for Empirical Spectral Measures: A Soft Approachn for many models, and there has been significant recent progress in obtaining more quantitative, non-asymptotic results. In this paper, we describe a systematic approach to bounding rates of convergence and proving tail inequalities for the empirical spectral measures of a wide variety of random ma

小故事

Concentration of Measure Without Independence: A Unified Approach Via the Martingale Methodo any of its individual arguments will tend to take values very close to its expectation. This phenomenon is most completely understood when the arguments are mutually independent random variables, and there exist several powerful complementary methods for proving concentration inequalities, such as

缺乏

Strong Data-Processing Inequalities for Channels and Bayesian Networksverse) results in information theory and many other disciplines. Various channel-dependent improvements (called strong data-processing inequalities, or SDPIs) of this inequality have been proposed both classically and more recently. In this note we first survey known results relating various notions

Sigmoidoscopy

Cacophonous

出生

Non-standard Constructions in Convex Geometry: Geometric Means of Convex Bodiess which were not previously considered in convex geometry. We illustrate this philosophy by describing a recent result of Molchanov, who constructed continued fractions of convex bodies..Our main construction is the geometric mean of two convex bodies. We define it using the above ideology, and disc

为敌

Randomized Isoperimetric Inequalitiesaló, Busemann-Petty and their various extensions. We show that many such inequalities admit stronger randomized forms in the following sense: for natural families of associated random convex sets one has stochastic dominance for various functionals such as volume, surface area, mean width and others

BAIL

Forward and Reverse Entropy Power Inequalities in Convex Geometryinequality. Motivated by this connection to Convex Geometry, we survey various recent developments on forward and reverse entropy power inequalities not just for the Shannon-Boltzmann entropy but also more generally for Rényi entropy. In the process, we discuss connections between the so-called func