1. Lyapunov conditions for Super Poincaré inequalities
- Author
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Feng-Yu Wang, Liming Wu, Patrick Cattiaux, Arnaud Guillin, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Centre National de la Recherche Scientifique (CNRS), School of Mathematical Sciences [Beijing] (SMS), Beijing Normal University (BNU), Institute of Applied Mathematics, Chinese Academy of Sciences [Beijing] (CAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Lyapunov function ,Pure mathematics ,Poincaré inequality ,Markov process ,Super Poincaré inequalities ,01 natural sciences ,010104 statistics & probability ,symbols.namesake ,Euclidean geometry ,Ergodic theory ,[MATH]Mathematics [math] ,0101 mathematics ,Logarithmic Sobolev inequalities ,ComputingMilieux_MISCELLANEOUS ,Lyapunov functions ,Mathematics ,010102 general mathematics ,Mathematical analysis ,46E35 35A25 46N30 60J35 60J60 ,Poincaré inequalities ,Sobolev space ,Rate of convergence ,Ergodic processes ,Poincaré conjecture ,symbols ,Analysis - Abstract
We show how to use Lyapunov functions to obtain functional inequalities which are stronger than Poincaré inequality (for instance logarithmic Sobolev or F-Sobolev). The case of Poincaré and weak Poincaré inequalities was studied in [D. Bakry, P. Cattiaux, A. Guillin, Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincaré, J. Funct. Anal. 254 (3) (2008) 727–759. Available on Mathematics arXiv:math.PR/0703355, 2007]. This approach allows us to recover and extend in a unified way some known criteria in the euclidean case (Bakry and Emery, Wang, Kusuoka and Stroock, …).
- Published
- 2009
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