A semidefinite bound for mixing rates of Markov chains

Random Structures and Algorithms

Volumn 11, Issue 4, 1997, Pages 299-313

  Kahale, Nabil ^a  

^a AT AND T LABS RESEARCH   (United States)

Author keywords

Eigenvalues; Markov chains; Multi commodity flow; Poincar inequalities; Semidefinite programming

Indexed keywords

EID: 0031481570     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2418(199712)11:4<299::AID-RSA2>3.0.CO;2-U     Document Type: Article

References (22)

1. D. Aldous and J. Fill, Reversible Markov Chains and Random Walks on Graphs, to appear.
2. N. Alon, Eigenvalues and expanders, Combinatorica, 6, 83-96 (1986).
3. P. Diaconis and L. Saloff-Coste, personal communication, 1995.
4. P. Diaconis and L. Saloff-Coste, Comparison theorems for reversible Markov Chains, Ann. Appl. Probab., 3, 696-730 (1993).
5. P. Diaconis and L. Saloff-Coste, Nash inequalities for finite Markov chains, preprint, 1995.
6. P. Diaconis and L. Saloff-Coste, What do we know about the Metropolis algorithm? In 27th Annual ACM Symposium on Theory of Computing, ACM Press, New York, 1995, pp. 112-129.
7. P. Diaconis and D. Stroock, Geometric bounds for eigenvalues of Markov chains, Ann. Appl. Probab., 1, 36-61 (1991).
8. J. Fill, unpublished manuscript, July 1990.
9. J. Fill, Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains with an application to the exclusion process, Ann. Appl. Probab., 1, 62-87 (1991).
10. M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman and Company, San Fransisco, 1979.
11. S. Guattery and G. Miller, personal communication, 1994.
12. M. Grötschel, L. Lovász, and A. Schrijver, The ellipsoid method and its consequences in combinatorial optimization, Combinatorica, 1, 169-197 (1981).
13. R. Horn and C. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985.
14. M. Jerrum and A. Sinclair, Approximating the permanent, SIAM J. Comput., 18, 1149-1178 (1989).
15. N. Linial, E. London, and Y. Rabinovich, The geometry of graphs and some of its algorithmic applications, Combinatorica, 15, 215-245 (1995).
16. L. Lovász and M. Simonovits, Random walks in a convex body and an improved volume algorithm, Random Structures Algorithms, 4, 359-412 (1993).
17. E. Seneta, Non-Negative Matrices and Markov Chains, Springer-Verlag, Berlin, 1981.
18. A. Sinclair, Improved bounds for mixing rates of Markov chains and multicommodity flow, Combin. Probab. Comput., 1, 351-370 (1992).
19. A. Sinclair and M. Jerrum, Approximate counting, uniform generation, and rapidly mixing Markov chains, Inform. and Comput. 82, 93-113 (1989).
20. A. D. Sokal, Optimal Poincaré inequalities for the spectra of Markov chains, unpublished manuscript, September 1992.
21. L. Vandenberghe and S. Boyd, Semidefinite programming, SIAM Rev. 38, 49-95 (1996).
22. G. A. Watson, Characterization of the subdifferential of some matrix norms, Linear Algebra Appl., 170, 33-45 (1992).