The Borell–Ehrhard game

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6 Scopus citations


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 languageEnglish (US)
Pages (from-to)555-585
Number of pages31
JournalProbability Theory and Related Fields
Issue number3-4
StatePublished - Apr 2018

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Convexity
  • Ehrhard inequality
  • Gaussian measures
  • Stochastic games


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