Loading [MathJax]/extensions/MathMenu.js
Glauber dynamics on trees and hyperbolic graphs | IEEE Conference Publication | IEEE Xplore

Glauber dynamics on trees and hyperbolic graphs


Abstract:

We study discrete time Glauber dynamics for random configurations with local constraints (e.g. proper coloring, Ising and Potts models) on finite graphs with n vertices a...Show More

Abstract:

We study discrete time Glauber dynamics for random configurations with local constraints (e.g. proper coloring, Ising and Potts models) on finite graphs with n vertices and of bounded degree. We show that the relaxation time (defined as the reciprocal of the spectral gap 1-/spl lambda//sub 2/) for the dynamics on trees and on certain hyperbolic graphs, is polynomial in n. For these hyperbolic graphs, this yields a general polynomial sampling algorithm for random configurations. We then show that if the relaxation time /spl tau//sub 2/ satisfies /spl tau//sub 2/=O(n), then the correlation coefficient, and the mutual information, between any local function (which depends only on the configuration in a fixed window) and the boundary conditions, decays exponentially in the distance between the window and the boundary. For the Ising model on a regular tree, this condition is sharp.
Date of Conference: 08-11 October 2001
Date Added to IEEE Xplore: 07 August 2002
Print ISBN:0-7695-1390-5
Print ISSN: 1552-5244
Conference Location: Newport Beach, CA, USA

Contact IEEE to Subscribe

References

References is not available for this document.