Calculus of Variations and Geometric Measure Theory
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N. Gigli - M. Ledoux

From log Sobolev to Talagrand: a quick proof

created by gigli on 17 Nov 2011
modified on 02 Mar 2012


Accepted Paper: DCDS-A

Inserted: 17 nov 2011
Last Updated: 2 mar 2012

Year: 2011


We provide yet another proof of the Otto-Villani theorem from the log Sobolev inequality to the Talagrand transportation cost inequality valid in arbitrary metric measure spaces. The argument relies on the recent development 2 identifying gradient flows in Hilbert space and in Wassertein space, emphasizing one key step as precisely the root of the Otto-Villani theorem. The approach does not require the doubling property or the validity of the local Poincare' inequality.


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