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A covariance representation and an elementary proof of the Gaussian concentration inequality

Christian Houdré

Abstract

Via a covariance representation based on characteristic functions, a known elementary proof of the Gaussian concentration inequality is presented. A few other applications are briefly mentioned.

A covariance representation and an elementary proof of the Gaussian concentration inequality

Abstract

Via a covariance representation based on characteristic functions, a known elementary proof of the Gaussian concentration inequality is presented. A few other applications are briefly mentioned.

Paper Structure

This paper contains 1 theorem, 24 equations.

Key Result

Lemma 1

In ${\mathbb R}^d$, let $X\sim N(\mu,\Sigma)$ and let $f,g:{\mathbb R}^d\to {\mathbb R}$ be such that $\|\nabla f\|_\infty < +\infty$ and $\|\nabla g\|_\infty <+\infty$. Then where

Theorems & Definitions (1)

  • Lemma 1