English

Two-dimensional random interlacements: 0-1 law and the vacant set at criticality

Probability 2023-12-07 v2

Abstract

We correct and streamline the proof of the fact that, at the critical point α=1\alpha=1, the vacant set of the two-dimensional random interlacements is infinite (Comets, Popov, 2017). Also, we prove a zero-one law for a natural class of tail events related to the random interlacements.

Keywords

Cite

@article{arxiv.2209.07938,
  title  = {Two-dimensional random interlacements: 0-1 law and the vacant set at criticality},
  author = {Orphée Collin and Serguei Popov},
  journal= {arXiv preprint arXiv:2209.07938},
  year   = {2023}
}

Comments

revised version, 14 pages, 2 pictures; corrects a flaw contained in the final part of the proof in arXiv:1606.05805