Random interlacements on Galton-Watson Trees

Martin Tassy (Brown University)

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.

Full Text: Download PDF | View PDF online (requires PDF plugin)

Pages: 562-571

Publication Date: November 21, 2010

DOI: 10.1214/ECP.v15-1586

References

  1. R. Lyons and Y. Peres. Probability on trees and networks http://www.math.upenn.edu/~pemantle/Lectures/lec5.3-russ-yuval.pdf. Math. Review number not available.
  2. Sznitman, Alain-Sol. Vacant set of random interlacements and percolation. Ann. of Math. (2) 171 (2010), no. 3, 2039--2087. MR2680403
  3. Teixeira, A. Interlacement percolation on transient weighted graphs. Electron. J. Probab. 14 (2009), no. 54, 1604--1628. MR2525105 (Review)
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.