The Borell–Ehrhard game

Ramon van Handel

doi:10.1007/s00440-017-0762-4

The Borell–Ehrhard game

Ramon van Handel

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

A precise description of the convexity of Gaussian measures is provided by sharp Brunn–Minkowski type inequalities due to Ehrhard and Borell. We show that these are manifestations of a game-theoretic mechanism: a minimax variational principle for Brownian motion. As an application, we obtain a Gaussian improvement of Barthe’s reverse Brascamp–Lieb inequality.

Original language	English (US)
Pages (from-to)	555-585
Number of pages	31
Journal	Probability Theory and Related Fields
Volume	170
Issue number	3-4
DOIs	https://doi.org/10.1007/s00440-017-0762-4
State	Published - Apr 2018

All Science Journal Classification (ASJC) codes

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Convexity
Ehrhard inequality
Gaussian measures
Stochastic games

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10.1007/s00440-017-0762-4

Cite this

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AB - A precise description of the convexity of Gaussian measures is provided by sharp Brunn–Minkowski type inequalities due to Ehrhard and Borell. We show that these are manifestations of a game-theoretic mechanism: a minimax variational principle for Brownian motion. As an application, we obtain a Gaussian improvement of Barthe’s reverse Brascamp–Lieb inequality.

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KW - Gaussian measures

KW - Stochastic games

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ER -

The Borell–Ehrhard game

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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