A general lower bound for mixing of single-site dynamics on graphs

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn 2005, Issue , 2005, Pages 511-520

  Hayes, Thomas P ^a   Sinclair, Alistair ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDED DEGREE GRAPH; GLAUBER DYNAMICS; ISING MODEL; LOWER BOUND;

ALGORITHMS; COMPUTATIONAL METHODS; LINEAR EQUATIONS; MARKOV PROCESSES; PROBLEM SOLVING; STATISTICAL METHODS; THEOREM PROVING;

GRAPH THEORY;

EID: 33748590796     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/SFCS.2005.6     Document Type: Conference Paper

References (15)

1. D. Achlioptas, M. Molloy, C. Moore and F. van Bussel, "Sampling Grid Colourings with Fewer Colours," Proceedings of LATIN 2004, pp. 80-89.
2. D. Aldous, "Random walks on finite groups and rapidly mixing Markov chains," Séminaire de Probabilites XVII, Lecture Notes in Mathematics 986, pp. 243-297, Springer, Berlin, 1983.
3. D. Aldous and J. Fill, Reversible Markov chains and random walks on graphs, Unpublished manuscript. Chapter 3 dated September 10, 2002. Current version available at www.stat.berkeley.edu/users/aldous/RWG/book.html.
4. J. Besag, "Spatial interaction and the statistical analysis of lattice systems," Journal of the Royal Statistical Society Series B 36 (1974), pp. 192-236.
5. P. Diaconis and M. Shahshahani, "Generating a random permutation with random transpositions," Zeitschrift für Wahrscheinlichketistheorie und verwandte Gebiete 57 (1981), pp. 159-179.
6. P. Diaconis and L. Saloff-Coste, "Logarithmic Sobolev inequalities for finite Markov chains," Annals of Applied Probability 6, pp. 695-750.
7. M. Dyer, L.A. Goldberg, C. Greenhill, M. Jerrum and M. Mitzenmacher, "An extension of path coupling and its application to the Glauber dynamics for graph colourings," SIAM Journal on Computing 30 (2001), pp. 1962-1975.
8. M. Dyer, L.A. Goldberg and M. Jerrum, "Systematic scan for sampling colorings," Preprint, 2004, to appear in Annals of Applied Probability.
9. M. Dyer, A. Sinclair, E. Vigoda and D. Weitz, "Mixing in time and space for lattice spin systems: a combinatorial view," Random Structures & Algorithms 24 (2004), pp. 461-479.
10. T.P. Hayes and A. Sinclair, "A general lower bound for mixing of single-site dynamics on graphs," (Full version), arXiv:math.PR/0507517 (July 2005).
11. M. Jerrum, "A very simple algorithm for estimating the number of k-colourings of a low-degree graph," Random Structures& Algorithms7(1995),pp. 157-165.
12. F. Martinelli and E. Olivieri, "Approach to equilibrium of Glauber dynamics in the one phase region I: The attractive case," Communications in Mathematical Physics 161 (1994), pp. 447-486.
13. J. Moussouris, "Gibbs and Markov random systems with constraints," Journal of Statistical Physics 10 (1974), pp. 11-33.
14. E. Vigoda, "Improved bounds for sampling colorings," Journal of Mathematical Physics 41 (2000), pp. 1555-1569.
15. E. Vigoda, "A note on the Glauber dynamics for sampling independent sets," Electronic Journal of Combinatorics 8(1) (2001).