The Annals of Applied Probability

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 ℤd 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*.

Article information

Source
Ann. Appl. Probab., Volume 19, Number 1 (2009), 454-466.

Dates
First available in Project Euclid: 20 February 2009

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1235140345

Digital Object Identifier
doi:10.1214/08-AAP547

Mathematical Reviews number (MathSciNet)
MR2498684

Zentralblatt MATH identifier
1158.60046

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C41: Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50]

Keywords
Random walks percolation random interlacements

Citation

Teixeira, Augusto. On the uniqueness of the infinite cluster of the vacant set of random interlacements. Ann. Appl. Probab. 19 (2009), no. 1, 454--466. doi:10.1214/08-AAP547. https://projecteuclid.org/euclid.aoap/1235140345


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References

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