English

Widths of crossings in Poisson Boolean percolation

Probability 2025-04-30 v1

Abstract

We answer the following question: if the occupied (or vacant) set of a planar Poisson Boolean percolation model does contain a crossing of an n×nn\times n square, how wide is this crossing? The answer depends on the whether we consider the critical, sub- or super-critical regime, and is different for the occupied and vacant sets.

Cite

@article{arxiv.2211.11661,
  title  = {Widths of crossings in Poisson Boolean percolation},
  author = {Ioan Manolescu and Leonardo V. Santoro},
  journal= {arXiv preprint arXiv:2211.11661},
  year   = {2025}
}
R2 v1 2026-06-28T06:23:45.986Z