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

By Augusto Teixeira. 2008

69 citations recorded by the source corpus.

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

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/29b67b420184583257b14aa6974bbf1e26fdfbdd

How researchers see this paper

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In Mathematical Physics

1. Serguei Popov
2. A. Sznitman
3. Augusto Teixeira
4. Ofer Zeitouni
5. David Belius
6. Francis Comets
7. Yuval Peres

In Statistics and Probability

1. Serguei Popov
2. A. Sznitman
3. Augusto Teixeira
4. David Belius

Citations in the corpus

• Soft local times and decoupling of random interlacements (2012, background): “Moreover, it is also proved that if existent, the infinite connected component of the vacant set must be unique, see [29], Theorem 1.”
• On the size of a finite vacant cluster of random interlacements with small intensity (2010, background): “Mathematics Subject Classification (2000) 60K35 · 82C41”
• Vacant Set of Random Interlacements and Percolation (2007, background): “The results presented here have triggered some progress on the questions mentioned above; see in particular [15], [20], [21], [22], and [25].”