Mixing times for uniformly ergodic Markov chains

Stochastic Processes and their Applications

Volumn 71, Issue 2, 1997, Pages 165-185

  Aldous, David ^a   Lovász, László ^b   Winkler, Peter ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b Yale University   (United States)

^c LUCENT TECHNOLOGIES   (United States)

Author keywords

Markov chain; Minorization; Mixing time; Randomized algorithm; Stopping time

Indexed keywords

EID: 0031573364     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(97)00037-9     Document Type: Article

References (32)

1. Aldous, D. J., 1982. Some inequalities for reversible Markov chains. J. London Math. Soc. (2), 25, 564-576.
2. Aldous D. J., Fill, J. A., 1997. Reversible Markov Chains and Random Walks on Graphs. Book in preparation.
3. Baxter J. R., Chacon, R. V., 1976. Stopping times for recurrent Markov processes. Illinois J. Math. 20, 467-475.
4. Bayer, D., Diaconis, P., 1992. Trailing the dovetail shuffle to its lair, Ann. Appl. Probab 2, 294-313.
5. Chung, F. R. K., Graham, R. L., 1996. Stratified random walks on the n-cube. Technical report, Univ. Pennsylvania.
6. Dellacherie, C. Meyer, P.-A., 1983. Probabilités et Potentiel: Théorie Discrète du Potentiel. Hermann, Paris.
7. Diaconis, P., 1988. Group Representations in Probability and Statistics. Institute of Mathematical Statistics, Hayward, CA.
8. Diaconis, P., 1996. The cut-off phenomenon in finite Markov chains. Proc. Nat. Acad. Sci. USA 93, 1659-1664.
9. Diaconis, P., Fill, J. A., 1990. Strong stationary times via a new form of duality. Ann. Probab. 18, 1483-1522.
10. Diaconis P., Saloff-Coste, L., 1996. Nash inequalities for finite Markov chains. J. Theoret. Probab. 9, 459-510.
11. Diaconis, P., Saloff-Coste, L., 1996. Walks on generating sets of groups. Probab. Theory Related Fields 105, 393-421.
12. Dinges, H., 1974. Stopping sequences. In: Séminaire de Probabilités VIII, Lecture Notes in Math., vol. 381, Springer, Berlin, pp. 27-36.
13. Frieze, A., Kannan, R., Polson, N., 1994. Sampling from log-concave distributions. Ann. Appl. Probab. 4, 812-837.
14. Goldstein, S., 1979. Maximal coupling. Z. Wahrsch. Verw. Gebiete 46, 193-204.
15. Jerrum M., Sinclair, A., 1989. Approximating the permanent. SIAM J. Comput. 18, 1149-1178.
16. 5) volume algorithm. Random Struct. Alg. 8, to appear.
17. Kemeny, J.G., Snell, J.L., 1960. Finite Markov Chains. Van Nostrand, Princeton, NJ.
18. Lindvall, T., 1992. Lectures on the Coupling Method. Wiley, New York.
19. Lovász, L., Simonovits, M., 1993. Random walks in a convex body and an improved volume algorithm. Random Struct. Alg. 4, 359-412.
20. Lovász, L., Winkler, P., 1995. Efficient stopping rules for Markov chains. In: Proc. 27th ACM Symp. Theory of Computing, pp. 76-82.
21. Lovász, L., Winkler, P., 1997. Fast mixing in a Markov chain. In preparation.
22. Lovász, L., Winkler, P., 1997. Reversal of Markov chains and the forget time. In preparation.
23. Meyn, S.P., Tweedie, R.L., 1993. Markov Chains and Stochastic Stability. Springer, Berlin.
24. Motwani, R., Raghavan, P., 1995. Randomized Algorithms. Cambridge University Press, Cambridge.
25. Nummelin, E., 1984. General Irreducible Markov Chains and Non-Negative Operators. Cambridge University Press, Cambridge.
26. Orey, S., 1971. Limit Theorems for Markov Chain Transition Probabilities. Van Nostrand, Princeton, NJ.
27. Pitman, J.W., 1977. Occupation measures for Markov chains. Adv. Appl. Probab. 9, 69-86.
28. Revuz, D., Remarks on the filling scheme for recurrent Markov chains. Duke Math. J. 45, 681-689.
29. Revuz, D., 1984. Markov Chains, 2nd ed. North-Holland, Amsterdam.
30. Rost, H., 1971. The stopping distributions of a Markov process. Invent. Math. 14, 1-16.
31. Sinclair, A.J., 1993. Algorithms for Random Generation and Counting. Birkhauser, Basel.
32. Syski, R., 1992. Passage Times for Markov Chains. IOS Press, Amsterdam.