@article{EJP670,
author = {Augusto Teixeira},
title = {Interlacement percolation on transient weighted graphs},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {14},
year = {2009},
keywords = {random walks, random interlacements, percolation},
abstract = {In this article, we first extend the construction of random interlacements, introduced by A.S. Sznitman in [14], to the more general setting of transient weighted graphs. We prove the Harris-FKG inequality for this model and analyze some of its properties on specific classes of graphs. For the case of non-amenable graphs, we prove that the critical value $u_*$ for the percolation of the vacant set is finite. We also prove that, once $\mathcal{G}$ satisfies the isoperimetric inequality $I S_6$ (see (1.5)), $u_*$ is positive for the product $\mathcal{G} \times \mathbb{Z}$ (where we endow $\mathbb{Z}$ with unit weights). When the graph under consideration is a tree, we are able to characterize the vacant cluster containing some fixed point in terms of a Bernoulli independent percolation process. For the specific case of regular trees, we obtain an explicit formula for the critical value $u_*$.},
pages = {no. 54, 1604-1627},
issn = {1083-6489},
doi = {10.1214/EJP.v14-670},
url = {http://ejp.ejpecp.org/article/view/670}}