English

Random interlacements on Galton-Watson Trees

Probability 2010-12-06 v2

Abstract

We study the critical parameter u^{*} of random interlacements percolation (introduced by A.S Sznitman in arXiv:0704.2560) on a Galton-Watson tree conditioned on the non-extinction event. Starting from the previous work of A. Teixeira in arXiv:0907.0316, 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.

Keywords

Cite

@article{arxiv.1006.1597,
  title  = {Random interlacements on Galton-Watson Trees},
  author = {Martin Tassy},
  journal= {arXiv preprint arXiv:1006.1597},
  year   = {2010}
}

Comments

10 pages

R2 v1 2026-06-21T15:33:30.495Z