Slow mixing of glauber dynamics for the hard-core model on regular bipartite graphs

Random Structures and Algorithms

Volumn 28, Issue 4, 2006, Pages 427-443

  Calvin, David ^a   Tetali, Prasad ^b  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b Georgia Institute of Technology   (United States)

Author keywords

Conductance; Discrete Hypercube; Glauber Dynamics; Hard Core Model; Mixing Time

Indexed keywords

EID: 33745697550     PISSN: 10429832     EISSN: 10982418     Source Type: Journal    
DOI: 10.1002/rsa.20094     Document Type: Article

References (22)

1. J. van den Berg and J. E. Steif, Percolation and the hard-core lattice gas model, Stochastic Process Appl 49 (1994), 179-197.
2. S. Bezrukov, On minimization of the surrounding of subsets in Hamming space, Kombinatorno-algebraic methods in applied mathematics. Gorky University Press, Gorky, (1985), 45-48 (in Russian).
3. B. Bollobás, Modern graph theory, Springer, New York, 1998.
4. B. Bollobás, Random graphs, Cambridge University Press, Cambridge, 2001.
5. C. Borgs, J. Chayes, A. Frieze, J. H. Kim, P. Tetali, E. Vigoda, and V. Vu, Torpid mixing of some Monte Carlo Markov chain algorithms in statistical physics, Proc IEEE FOCS '99, (1999), 218-229.
6. H. Chernoff, A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations, Ann Math Stat 23 (1952), 493-507.
7. R. Diestel, Graph theory, Springer, New York, 2000.
8. R. L. Dobrushin, The problem of uniqueness of a Gibbs random field and the problem of phase transition, Funct Anal Appl 2 (1968), 302-312.
9. M. Dyer, A. Frieze, and M. Jerrum, On counting independent sets in sparse graphs, SIAM J Comput 31 (2002), 1527-1541.
10. D. Galvin, On homomorphisms from the Hamming cube to ℤ, Israel J Math 138 (2003), 189-213.
11. D. Galvin, Slow mixing of local dynamics for independent sets on the discrete torus, in preparation.
12. d, Combin Probab Comput 13 (2004), 137-164.
13. M. Jerrum and A. Sinclair, "The Monte Carlo Markov chain method: An approach to approximate counting and integration," Approximation alorithms for NP-hard problems, Ed. D. S. Hochbaum. PWS, 1996, 482-520.
14. F. Kelly, Loss networks, Ann Appl Probab 1 (1991), 319-378.
15. J. Körner and V. Wei, Odd and even Hamming spheres also have minimum boundary, Discrete Math 51 (1984), 147-165.
16. A.D. Korshunov and A. A. Sapozhenko, The number of binary codes with distance 2, Problemy Kibernet 40 (1983), 111-130 (in Russian).
17. L. Lovász, On the ratio of optimal integral and fractional covers, Discrete Math 13 (1975), 383-390.
18. A.A. Sapozhenko, On the number of connected subsets with given cardinality of the boundary in bipartite graphs, Melody Diskret Analiz 45 (1987), 42-70 (in Russian).
19. A. A. Sapozhenko, The number of antichains in ranked partially ordered sets, Diskret Mat 1 (1989), 74-93
20. (in Russian; translation in Discrete Math Appl 1(1) (1991), 35-58).
21. S. K. Stein, Two combinatorial covering theorems, J Combin Theory Ser A 16 (1974), 391-397.
22. E. Vigoda, A note on the Glauber dynamics for sampling independent sets, Electron J Combin 8(1) (2001), #R8.