On logarithmic Sobolev inequalities for continuous time random walks on graphs

Probability Theory and Related Fields

Volumn 116, Issue 4, 2000, Pages 573-602

  Ané, Cécile ^a   Ledoux, Michel ^a  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 19544378332     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400050263     Document Type: Article

References (15)

1. Aida, S., Elworthy, K.D.: Differential calculus on path and loop spaces I. Logarithmic Sobolev inequalities on path spaces. C. R. Acad. Sci. Paris, 321, 97-102 (1995)
2. Bakry, D.: L'hypercontractivité et son utilisation en théorie des semigroupes. Ecole d'Eté de Probabilités de St-Flour. Lecture Notes in Math., 1581, 1-114 (1994). Springer
3. Bakry, D.: On Sobolev and logarithmic Sobolev inequalities for Markov semigroups. New trends in Stochastic Analysis, 43-75 (1997). World Scientific
4. Bismut, J.-M.: Large deviations and the Malliavin calculus. Birkhäuser 1984
5. Brémaud, P.: Point processes and queues, Martingales dynamics. Springer 1981
6. Bobkov, S., Ledoux, M.: On modified logarithmic Sobolev inequalities for Bernoulli and Poisson measures. J. Funct. Anal., 156, 347-365 (1998)
7. Capitaine, M., Hsu, E.-P., Ledoux, M.: Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces. Elect. Comm. Prob., 2, Paper 7 (1997)
8. Gross, L.: Logarithmic Sobolev inequalities. Amer. J. Math., 97, 1060-1083 (1975)
9. Gross, L., Rothaus, O.: Herbst inequalities for supercontractive semigroups. Preprint (1997)
10. Hsu, E.P.: Logarithmic Sobolev inequalities on path spaces over Riemannian manifolds. Commun. Math. Phys., 189, 9-16 (1997)
11. Ledoux, M.: Concentration of measures and logarithmic Sobolev inequalities. Séminaire de Probabilités XXXIII. Lecture Notes in Math., 1709, 120-216 (1999). Springer
12. Pang, M.M.H.: Heat kernels of graphs. J. London Math. Soc., 47, 50-64 (1993)
13. Picard, J.: Formules de dualité sur l'espace de Poisson. Ann. Inst. H. Poincaré, 32, 509-548 (1996)
14. Saloff-Coste, L.: Lectures on finite Markov chains. Ecole d'Eté de Probabilités de St-Flour 1996. Lecture Notes in Math., 1665, 301-413 (1997). Springer
15. 1 and modified logarithmic Sobolev inequalities and deviation inequalities for Poisson point processes. Preprint (1998)