Geodesic
Short Probabilistic Proof of the Brascamp-Lieb and Barthe Theorems
Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 585-597

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DOI

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 Prèkopa-Leindler inequality and applies also to the reversed Brascamp-Lieb inequality, due to Barthe.
DOI : 10.4153/CMB-2013-040-x
Mots-clés : 39B62, 60J65, functional inequalities, Brownian motion 
Lehec, Joseph. Short Probabilistic Proof of the Brascamp-Lieb and Barthe Theorems. Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 585-597. doi: 10.4153/CMB-2013-040-x
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     title = {Short {Probabilistic} {Proof} of the {Brascamp-Lieb} and {Barthe} {Theorems}},
     journal = {Canadian mathematical bulletin},
     pages = {585--597},
     year = {2014},
     volume = {57},
     number = {3},
     doi = {10.4153/CMB-2013-040-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-040-x/}
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