Electronic Communications in Probability

Random interlacements on Galton-Watson Trees

Martin Tassy

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Abstract

We study the critical parameter $u^*$ of random interlacements on a Galton-Watson tree conditioned on the non-extinction event. We show that, for a given law of a Galton-Watson tree, the value of this parameter is a.s. constant and non-trivial. We also characterize this value as the solution of a certain equation.

Article information

Source
Electron. Commun. Probab., Volume 15 (2010), paper no. 50, 562-571.

Dates
Accepted: 21 November 2010
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465243993

Digital Object Identifier
doi:10.1214/ECP.v15-1586

Mathematical Reviews number (MathSciNet)
MR2737713

Zentralblatt MATH identifier
1226.60121

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60K37: Processes in random environments

Keywords
Random Interlacement Galton-Watson tree critical behaviour

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Tassy, Martin. Random interlacements on Galton-Watson Trees. Electron. Commun. Probab. 15 (2010), paper no. 50, 562--571. doi:10.1214/ECP.v15-1586. https://projecteuclid.org/euclid.ecp/1465243993


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References

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