A note on spatial monotonicity for one-dimensional spin systems
Probability
2015-10-13 v1
Abstract
We show that attractive, translation invariant, one-dimensional spin systems started from the unit step function possess the following basic property. At any time, the entire configuration from a point onward is stochastically decreasing with respect to distance from this point to the origin. The proof relies on a stochastic domination argument which exploits the interaction assumptions in a simple manner.
Cite
@article{arxiv.1510.03363,
title = {A note on spatial monotonicity for one-dimensional spin systems},
author = {Achillefs Tzioufas},
journal= {arXiv preprint arXiv:1510.03363},
year = {2015}
}