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