Evolving sets and mixing

Conference Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2003, Pages 279-286

  Morris, Ben ^a   Peres, Yuval ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Conductance; Markov chain; Martingale; MCMC; Mixing time

Indexed keywords

MARKOV PROCESSES; PROBABILITY; SET THEORY;

CONDUCTANCE BOUNDS;

COMPUTATIONAL METHODS;

EID: 0037770108     PISSN: 07349025     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/780583.780585     Document Type: Conference Paper

References (23)

1. Alon, N. (1986) Eigenvalues and expanders. Combinatorica 6, 83-96.
2. 1, Isoperimetric inequalities for graphs and superconcentrators, J. Combinatorial Theory Ser. B 38, 73-88.
3. Benjamini, I. and Mossel, E. (2002) On the mixing time of a simple random walk on the super critical percolation cluster. Probab. Th. Rel. Fields, to appear.
4. Chung, F. R. K. (1996) Laplacians of graphs and Cheeger's inequalities. In Combinatorics, Paul Erdös is eighty, Vol. 2 157-172, J. Bolyai Soc. Math. Stud., Budapest.
5. Chung, F. R. K. and Yau, S. T. (1995) Eigenvalues of graphs and Sobolev inequalities, Combinatorics, Probability and Computing 4, 11-26.
6. Coulhon, T. (1996). Ultracontractivity and Nash type inequalities. J. Fund. Anal. 141, 510-539.
7. Coulhon, T., Grigorýan, A. and Pittet, C. (2001). A geometric approach to on-diagonal heat kernel lower bounds on groups. Ann. Inst. Fourier (Grenoble) 51, 1763-1827.
8. Diaconis, P. and Saloff-Coste, L. (1996). Nash inequalities for finite Markov chains. J. Theoret. Probab. 9, 459-510.
9. Fill, J. A. (1991). Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process. Ann. Appl. Probab. 1, 62-87.
10. Häggström, O. and Jonasson, J. (1997). Rates of convergence for lamplighter processes. Stochastic Process. Appl. 67, 227-249.
11. Houdré, C. and Tetali, P. (2001). Isoperimetric Invariants for Product Markov Chains and Graph Products Combinatorica, to appear.
12. Jerrum, M. R. and Sinclair, A. J. (1989). Approximating the permanent. SIAM Journal on Computing 18, 1149-1178.
13. Kannan, R. (2002). Rapid Mixing in Markov Chains Proceedings of International Congress of Math. 2002, Vol. III, 673-683.
14. 2 spectrum for Markov chains and Markov processes: a generalization of Cheeger's inequality. Trans. Amer. Math. Soc. 309, 557-580.
15. Lovász, L. and R. Kannan, R. (1995). Faster mixing via average conductance Proceedings of the 27th Annual ACM Symposium on theory of computing.
16. Mathieu, P. and Remy, E. (2003) Isoperimetry and heat kernel decay on percolation clusters. Ann. Probab., to appear.
17. Mihail, M. (1989). Conductance and convergence of Markov chains - A combinatorial treatment of expanders. Proceedings of the 30th Annual Conference on Foundations of Computer Science, 526-531.
18. Montenegro, R. and Son, J.-B. (2001) Edge Isoperimetry and Rapid Mixing on Matroids and Geometric Markov Chains, Proceedings of the 33rd Annual ACM Symposium on theory of computing.
19. Morris, B. (2002). A new, probabilistic approach to heat kernel bounds. Lecture at Sectional AMS meeting, Atlanta, GA, March 2002.
20. Pittet, C. and Saloff-Coste, L. (2002) A survey on the relationships between volume growth, isoperimetry, and the behavior of simple random walk on Cayley graphs, with examples. Unpublished manuscript, available at http://www.math.cornell.adu/̃lsc/lau.html
21. Saloff-Coste, L. (1997). Lectures on finite Markov chains. Lecture Notes in Math. 1665, Springer, Berlin, 301-413.
22. Sinclair, A. (1993) Algorithms for Random Generation and Counting: A Markov Chain Approach, Birkhäuser, Boston.
23. Woess, W. (2000). Random walks on infinite graphs and groups. Cambridge Tracts in Mathematics, 138. Cambridge University Press.