Random interlacements on Galton-Watson Trees

Details Random interlacements on Galton-Watson Trees Random interlacements on Galton-Watson Trees

2010-06-08

arxiv.org/abs/1006.1597v2

Electronic Communications in Probability, 15, 562-571 (2010)

Mathematics

Probability

10 pages

Scientific paper

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.

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