The Asymmetric One-Dimensional Constrained Ising Model
Probability
2015-06-26 v1 Mathematical Physics
math.MP
Abstract
We study a reversible one-dimensional spin system with Bernoulli(p) stationary distribution, in which a site can flip only if the site to its left is in state +1. Such models have been used as simple exemplars of systems exhibiting slow relaxation. We give fairly sharp estimates of the spectral gap as p decreases to zero. The method uses Poincare comparison with a long-range process which is analyzed by probabilistic methods (coupling, supermartingales).
Keywords
Cite
@article{arxiv.math/0110023,
title = {The Asymmetric One-Dimensional Constrained Ising Model},
author = {David Aldous and Persi Diaconis},
journal= {arXiv preprint arXiv:math/0110023},
year = {2015}
}
Comments
32 pages