From log Sobolev to Talagrand: A quick proof | Zendy

Nicola Gigli | Zendy; Michel Ledoux | Zendy

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From log Sobolev to Talagrand: A quick proof

Author(s) -

Nicola Gigli,

Michel Ledoux

Publication year - 2012

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2013.33.1927

Subject(s) - poincaré inequality , mathematics , sobolev inequality , hilbert space , measure (data warehouse) , sobolev space , metric space , metric (unit) , pure mathematics , combinatorics , discrete mathematics , mathematical analysis , inequality , computer science , operations management , database , economics

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 develop- ment [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 Poincaré inequality

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