Isoperimetric invariants for product markov chains and graph products

Combinatorica

Volumn 24, Issue 3, 2004, Pages 359-388

  Houdre C ^a,b   Tetali, P ^c  

^a UNIVERSITÉ PARIS EST CRÉTEIL   (France)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^c Georgia Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 6344246438     PISSN: 02099683     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00493-004-0023-x     Document Type: Article

References (27)

1. D. ALDOUS and J. FILL: Reversible Markov chains and random walks on graphs, Book in preparation.
2. 1, Isoperimetric inequalities for graphs, and super-concentrators, J. Combinatorial Theory, Series B 38 (1985), 73-88.
3. S. G. BOBKOV and F. GÖTZE: Discrete isoperimetric and Poincaré-type inequalities, Probab. Theory & Related Fields 114(2) (1999), 245-277.
4. S. G. BOBKOV and C. HOUDRÉ: Some connections between isoperimetry and Sobolev type inequalities, Mem. Amer. Math. Soc. 129 (1997), pp. viii+111.
5. S. G. BOBKOV and C. HOUDRÉ: Isoperimetric constants for product probability measures, Ann. Probab. 25 (1997), 184-205.
6. ∞, vertex isoperimetry and concentration, Combinatorica 20(2) (2000), 153-172.
7. B. BOLLOBÁS and I. LEADER: Compressions and isoperimetric inequalities, J. Combin. Theory Ser. A 56 (1991), 47-62.
8. B. BOLLOBÁS and I. LEADER: Isoperimetric inequalities and fractional set systems, J. Combin. Theory Ser. A 56 (1991), 63-74.
9. B. BOLLOBÁS and I. LEADER: Edge-isoperimetric inequalities in the grid, Combinatorica 11 (1991), 299-314.
10. C. COOPER, M. DYER, A. FRIEZE and R. RUE: Mixing properties of the Swendsen-Wang process on the complete graph and narrow grids, J. Math. Phys. 41 (2000), 1499-1527.
11. P. DIACONIS and L. SALOFF-COSTE: Logarithmic Sobolev inequalities and finite Markov chains, Ann. of Appl. Prob. 6 (1996), 695-750.
12. P. DIACONIS and D, STROOCK: Geometric bounds for eigenvalues of Markov chains, Ann. of Appl. Prob. 1 (1991), 36-61.
13. J. A. FILL: Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process, Ann. of Appl. Prob. 1 (1991), 62-87.
14. L. HARPER: Optimal numberings and isoperimetric problems on graphs, J. Combinatorial Theory 1 (1966), 385-393.
15. C. HOUDRÉ: Mixed and isoperimetric estimates on the log-Sobolev constants of graphs and Markov chains. Combinatorica 21(4) (2001), 489-513.
16. C. HOUDRÉ and P. TETALI: Isoperimetric constants for product Markov kernels and graph products, Manuscript (1996).
17. C. HOUDRÉ and P. TETALI: Concentration of measure for products of Markov chains via functional inequalities, Combinat. Probab. and Computing 10 (2001), 1-28.
18. M. JERRUM and A. SINCLAIR: Approximate counting, uniform generation, and rapidly mixing Markov chains, Information and Computation 82 (1989), 93-133.
19. N. KAHALE: A semidefinite bound for mixing rates of Markov chains, in Proceedings of the Workshop on Randomized Algorithms and Computation (Berkeley, CA, 1995); also Random Structures & Algorithms 11 (1997), 299-313.
20. 2 spectrum for Markov chains and Markov processes: A generalization of Cheeger's inequality, Trans. Amer. Math. Soc. 309 (1988), 557-580.
21. L. LOVÁSZ: Combinatorial Problems and Exercises, 1993 (second edition), North-Holland, Elsevier Science Publishers (Amsterdam) and Akadémiai Kiadó (Budapest).
22. G. A. MARGULIS: Probabilistic characteristics of graphs with large connectivity, Problemy Peredachi Informatsii 10 (1974), 101-108; English translation: Problems Info. Transmission 10 (1977), 174-179, Plenum Press, New York.
23. G. A. MARGULIS: Probabilistic characteristics of graphs with large connectivity, Problemy Peredachi Informatsii 10 (1974), 101-108; English translation: Problems Info. Transmission 10 (1977), 174-179, Plenum Press, New York.
24. B. MOHAR: Isoperimetric numbers of graphs, J. of Comb. Theory, Series B 47 (1989), 274-291.
25. T. STOYANOV: Doctoral Dissertation, School of Mathematics, Georgia Institute of Technology, Atlanta, GA (2001).
26. M. TALAGRAND: Isoperimetry, logarithmic Sobolev inequalities on the discrete cube, and Margulis' graph connectivity theorem, Geometric and Functional Analysis 3 (1993), 295-314.
27. J. P. TILLICH and G. ZÉMOR: Discrete isoperimetric inequalities and the probability of a decoding error, Combinat. Probab. and Computing 9 (2000), 465-479.