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FROM LOG SOBOLEV TO TALAGRAND: A QUICK PROOF
- Source :
- Discrete and Continuous Dynamical Systems-Series A, Discrete and Continuous Dynamical Systems-Series A, American Institute of Mathematical Sciences, 2013, pp.dcds.2013.33.xx, Discrete and Continuous Dynamical Systems-Series A, 2013, pp.dcds.2013.33.xx
- Publication Year :
- 2013
- Publisher :
- HAL CCSD, 2013.
-
Abstract
- International audience; 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.
- Subjects :
- Pure mathematics
log-Sobolev inequality
Space (mathematics)
[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]
01 natural sciences
Measure (mathematics)
Metric measure spaces
Sobolev inequality
010104 statistics & probability
symbols.namesake
Development (topology)
Settore MAT/05 - Analisi Matematica
Mathematics::Metric Geometry
Discrete Mathematics and Combinatorics
functional inequalities
0101 mathematics
[MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG]
Mathematics
Applied Mathematics
010102 general mathematics
Hilbert space
optimal transport
Talagrand inequality
Sobolev space
Poincaré conjecture
Metric (mathematics)
symbols
Analysis
Subjects
Details
- Language :
- English
- ISSN :
- 10780947
- Database :
- OpenAIRE
- Journal :
- Discrete and Continuous Dynamical Systems-Series A, Discrete and Continuous Dynamical Systems-Series A, American Institute of Mathematical Sciences, 2013, pp.dcds.2013.33.xx, Discrete and Continuous Dynamical Systems-Series A, 2013, pp.dcds.2013.33.xx
- Accession number :
- edsair.doi.dedup.....c55a4913fe60123e632c61d3e0730afc