141 citations · 238 across the 33 of their papers we have counts for
6 papers · 1 filter
A Gaussian small deviation inequality for convex functions
Grigoris Paouris, Petros Valettas
Let be an -dimensional Gaussian vector and let be a convex function. We show that: $$\mathbb P \left( f(Z) \leq \mathbb E f(Z) -t\sqrt{ {\rm V…
Probabilistic Condition Number Estimates For Real Polynomial Systems I: A Broader Family Of Distributions
Alperen A. Ergür, J. Maurice Rojas, Grigoris Paouris
We consider the sensitivity of real roots of polynomial systems with respect to perturbations of the coefficients. In particular - for a version of the condition number defined by…
Generalized Dual Sudakov Minoration via Dimension Reduction - A Program
Shahar Mendelson, Emanuel Milman, Grigoris Paouris
We propose a program for establishing a conjectural extension to the class of (origin-symmetric) log-concave probability measures , of the classical dual Sudakov Minoration on t…
Randomized isoperimetric inequalities
Grigoris Paouris, Peter Pivovarov
We discuss isoperimetric inequalities for convex sets. These include the classical isoperimetric inequality and that of Brunn-Minkowski, Blaschke-Santalo, Busemann-Petty and their…
An interpolation proof of Ehrhard's inequality
Joe Neeman, Grigoris Paouris
We prove Ehrhard's inequality using interpolation along the Ornstein-Uhlenbeck semi-group. We also provide an improved Jensen inequality for Gaussian variables that might be of ind…
An inequality for moments of log-concave functions on Gaussian random vectors
Nikos Dafnis, Grigoris Paouris
We prove a sharp moment inequality for a log-concave or a log-convex function, on Gaussian random vectors. As an application we take a stability result for the classical logarithmi…