English

Random interlacements on transient weighted graphs: 0-1 laws and FKG inequality

Probability 2026-03-12 v1

Abstract

We study some properties of the random interlacement model on a transient weighted graph, which was introduced by A. Teixeira in ["Interlacement percolation on transient weighted graphs", Augusto Teixeira, Electronic Journal of Probability (2009)]. We give a simple proof of the FKG-property and discuss the occurrence of several 0-1 laws for non-local events. We show in particular a 0-1 law for some increasing non-local events, without any assumption.

Keywords

Cite

@article{arxiv.2603.10896,
  title  = {Random interlacements on transient weighted graphs: 0-1 laws and FKG inequality},
  author = {Orphée Collin},
  journal= {arXiv preprint arXiv:2603.10896},
  year   = {2026}
}

Comments

Version 1 : 33 pages, no figure. Further version(s) will include illustrations, examples of applications and miscellaneous