Interlacement percolation on transient weighted graphs
By Augusto Teixeira. 2009
100 citations recorded by the source corpus.
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 $u_*$.
Subfields: Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/d68651672a641edbc4dd137a21ad1c2710537a65
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In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- Topics in Occupation Times and Gaussian Free Fields (2012, background): “4 of [27] and [29] for a more detailed description of the Poisson point process of random interlacements in this context.”