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arXiv · 0805.4106

On the uniqueness of the infinite cluster of the vacant set of random interlacements

Augusto Teixeira
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Abstract

We consider the model of random interlacements on $\mathbb{Z}^d$ introduced in Sznitman [Vacant set of random interlacements and percolation (2007) preprint]. For this model, we prove the uniqueness of the infinite component of the vacant set. As a consequence, we derive the continuity in $u$ of the probability that the origin belongs to the infinite component of the vacant set at level $u$ in the supercritical phase $u<u_*$.

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Augusto Teixeira. 2009-03-03. On the uniqueness of the infinite cluster of the vacant set of random interlacements. https://doi.org/10.1214/08-aap547

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