A modified version of frozen percolation on the binary tree

R. Brouwer

A modified version of frozen percolation on the binary tree

Probability 2007-05-23 v1

Authors: R. Brouwer

Abstract

We consider the following, intuitively described process: at time zero, all sites of a binary tree are at rest. Each site becomes activated at a random uniform [0,1] time, independent of the other sites. As soon as a site is in an infinite cluster of activated sites, this cluster of activated sites freezes. The main question is whether a process like this exists. Aldous [Ald00] proved that this is the case for a slightly different version of frozen percolation. In this paper we construct a process that fits the intuitive description and discuss some properties.

Keywords

percolation theory

Cite

@article{arxiv.math/0511021,
  title  = {A modified version of frozen percolation on the binary tree},
  author = {R. Brouwer},
  journal= {arXiv preprint arXiv:math/0511021},
  year   = {2007}
}

Comments

19 pages, 2 figures

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