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Short Probabilistic Proof of the Brascamp-Lieb and Barthe Theorems

  Published:2013-11-01
 Printed: Sep 2014
  • Joseph Lehec,
    Ceremade (UMR CNRS 7534), Université Paris-Dauphine, Place de Lattre de Tassigny, 75016 Paris, France
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Abstract

We give a short proof of the Brascamp-Lieb theorem, which asserts that a certain general form of Young's convolution inequality is saturated by Gaussian functions. The argument is inspired by Borell's stochastic proof of the Prékopa-Leindler inequality and applies also to the reversed Brascamp-Lieb inequality, due to Barthe.
Keywords: functional inequalities, Brownian motion functional inequalities, Brownian motion
MSC Classifications: 39B62, 60J65 show english descriptions Functional inequalities, including subadditivity, convexity, etc. [See also 26A51, 26B25, 26Dxx]
Brownian motion [See also 58J65]
39B62 - Functional inequalities, including subadditivity, convexity, etc. [See also 26A51, 26B25, 26Dxx]
60J65 - Brownian motion [See also 58J65]
 

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