Exponential decay of entropy in the random transposition and Bernoulli-Laplace models

Annals of Applied Probability

Volumn 13, Issue 4, 2003, Pages 1591-1600

  Gao, Fuqing ^a   Quastel, Jeremy ^b  

^a HUBEI UNIVERSITY   (China)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

Modified logarithmic Sobolev inequality; Time to stationarity

Indexed keywords

EID: 0346913244     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1069786512     Document Type: Article

References (18)

1. ANÉ, C. and LEDOUX, M. (2000). On logarithmic Sobolev inequalities for continuous random walks on graphs. Probab. Theory Related Fields 116 573-602.
2. BAKRY, D. (1994). L'hypercontactivite et son utilisation en theorie des semi-groupes. Lectures on Probability Theory. Lecture Notes in Math. 1581 1-114. Springer, Berlin.
3. BOBKOV, S. and LEDOUX, M. (1998). On modified logarithmic Sobolev inequalities for Bernoulli and Poisson measures J. Funct. Anal. 156 347-365.
4. DAI PRA, P., PAGANONI, A. and POSTA, G. (2002). Entropy inequality for unbounded spin systems. Am. Probab. 30 1959-1976.
5. DIACONIS, P. and SALOFF-COSTE, L. (1993). Comparison theorems for reversible Markov chains. Ann. Appl. Probab. 3 696-730.
6. DIACONIS, P. and SALOFF-COSTE, L. (1995). Random walks on finite groups: A survey of analytic techniques. In Probability Measures on Groups and Related Structures (H. Heyer, ed.) 44-75. World Scientific, Singapore.
7. DIACONIS, P. and SALOFF-COSTE, L. (1996). Logarithmic Sobolev inequalities for finite Markov chains. Ann. Appl. Probab. 6 695-750.
8. DIACONIS, P. and SHAHSHAHANI, M. (1981). Generating a random permutation with random transpositions. Z. Wahrsch. Verw. Gebiete 57 159-179.
9. DIACONIS, P. and SHAHSHAHANI, M. (1987). Time to reach stationarity in the Bernoulli-Laplace diffusion model. SIAM J. Math. Anal. 18 208-218.
10. DEUSCHEL, J. and STROOCK, D. W. (1989). Large Deviations. Academic Press, San Diego.
11. GROSS, L. (1976). Logarithmic Sobolev inequalities. Amer. J. Math. 97 1061-1083.
12. KIPNIS, C., OLLA, S. and VARADHAN, S. R. S. (1989). Hydrodynamics and large deviations for simple exclusion processes. Comm. Pure Appl. Math. 42 115-137.
13. LEDOUX, M. (1999). Concentration of measure and logarithmic Sobolev inequalities. Lecture Notes in Math. 1709 120-216. Springer, Berlin.
14. LEE, T. Y. and YAU, H. T. (1998). Logarithmic Sobolev inequality for some models of random walks. Ann. Probab. 26 1855-1873.
15. LU, S. and YAU, H. T. (1993). Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics. Comm. Math. Phys. 156 399-433.
16. QUASTEL, J. (1992). Diffusion of color in the simple exclusion process. Comm. Pure Appl. Math. 45 623-679.
17. WU, L. (2000). A new modified logarithmic Sobolev inequality for Poisson point processes and several applications. Probab. Theory Related Fields 118 427-438.
18. YAU, H. T. (1997). Logarithmic Sobolev inequality for generalized simple exclusion processes. Probab. Theory Related Fields 109 507-538.