Invariant monotone coupling need not exist
Probability
2013-05-27 v2
Abstract
We show by example that there is a Cayley graph, having two invariant random subgraphs X and Y, such that there exists a monotone coupling between them in the sense that , although no such coupling can be invariant. Here, "invariant" means that the distribution is invariant under group multiplications.
Cite
@article{arxiv.1011.2283,
title = {Invariant monotone coupling need not exist},
author = {Péter Mester},
journal= {arXiv preprint arXiv:1011.2283},
year = {2013}
}
Comments
Published in at http://dx.doi.org/10.1214/12-AOP767 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)