Blocking conductance and mixing in random walks

Combinatorics Probability and Computing

Volumn 15, Issue 4, 2006, Pages 541-570

  Kannan, R ^a   Lovasz L ^b   Montenegro, R ^c  

^a Yale University   (United States)

^b MICROSOFT RESEARCH   (United States)

^c GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; EQUATIONS OF STATE; GRAPH THEORY; MARKOV PROCESSES; SET THEORY;

DIAMETERS; NODE EXPANSION; RANDOM WALKS; SOBOLEV INEQUALITIES;

RANDOM PROCESSES;

EID: 33744953716     PISSN: 09635483     EISSN: 14692163     Source Type: Journal    
DOI: 10.1017/S0963548306007504     Document Type: Article

References (22)

1. Aldous, D. J. and Diaconis, P. (1986) Shuffling cards and stopping times. Amer. Math. Monthly 93 333-348.
2. Aldous, D. J., Lovász, L. and Winkler, P. (1997) Mixing times for uniformly ergodic Markov chains. Stochastic Process. Appl. 71 165-185.
3. Benjamini, I. and Mossel, E. (2003) On the mixing time of simple random walk on the super critical percolation cluster. Probab. Theory Rel. Fields 125 408-420.
4. Diaconis, P. and Saloff-Coste, L. (1996) Logarithmic Sobolev inequalities for finite Markov chains. Ann. Appl. Probab. 6 695-750.
5. Dyer, M. and Frieze, A. (1992) Computing the volume of convex bodies: A case where randomness provably helps. In Probabilistic Combinatorics and its Applications (B. Bollobás, ed.), AMS, pp. 123-169.
6. Dyer, M., Frieze, A. and Kannan, R. (1989) A random polynomial time algorithm for estimating volumes of convex bodies. In Proc. 21st Annual ACM Symposium on the Theory of Computing (STOC), pp. 375-381.
7. Frieze, A. and Kannan, R. (1999) Log-Sobolev inequalities and sampling from log-concave distributions. Ann. Appl. Probab. 9 14-26.
8. Jerrum, M. and Sinclair, A. (1988) Conductance and the rapid mixing property for Markov chains: The approximation of the permanent resolved. In Proc. 20th Annual ACM Symposium on Theory of Computing (STOC), pp. 235-243.
9. Jerrum, M. and Son, J. (2002) Spectral gap and log-Sobolev constant for balanced matroids. In Proc. 31st Annual IEEE Symposium on Foundations of Computer Science (FOCS), IEEE Computer Society, pp. 721-729.
10. Jerrum, M., Son, J., Tetali, P. and Vigoda, E. (2004) Elementary bounds on Poincaré and log-Sobolev constants for decomposable Markov chains. Ann. Appl. Probab. 14 1741-1765.
11. Kannan, R., Lovász, L. and Simonovits, M. (1995) Isoperimetric problems for convex bodies and a localization lemma. Discrete Comput. Geom. 13 541-559.
12. 5) volume algorithm. Random Struct. Alg. 11 1-50.
13. Ledoux, M. (1999) Concentration of measure and logarithmic Sobolev inequalities. In Séminaire de Probabilités XXXIII, Vol. 1709 of Lecture Notes in Mathematics, Springer, Berlin, pp. 120-216.
14. Lovász, L. and Kannan, R. (1999) A logarithmic Cheeger inequality and mixing in random walks. In Proc. 31st Annual ACM Symposium on Theory of Computing (STOC), pp. 282-287.
15. Lovász, L. and Simonovits, M. (1993) Random walks in a convex body and an improved volume algorithm. Random Struct. Alg. 4 359-412.
16. 4) volume algorithm. In Proc. 44th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 650-659.
17. Lovász, L. and Winkler, P. (1995) Efficient stopping rules for Markov chains. In Proc. 27th ACM Symposium on the Theory of Computing (STOC), pp. 76-82.
18. Montenegro, R. (2002) Faster mixing by isoperimetric inequalities. PhD Thesis, Department of Mathematics, Yale University.
19. Montenegro, R. (2005) Vertex and edge expansion properties for rapid mixing. Random Struct. Alg. 26 52-68.
20. Montenegro, R. (2006) A sharp isoperimetric inequality for convex bodies. Israel J. Math., to appear.
21. Morris, B. and Peres, Y. (2003) Evolving sets and mixing. In Proc. 35th Annual ACM Symposium on Theory of Computing (STOC), pp. 279-286.
22. Talagrand, M. (1993) Isoperimetry, logarithmic Sobolev inequalities on the discrete cube, and Margulis' graph connectivity theorem. Geom. Funct. Anal. 3 295-314.