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arXiv · 2211.11661

Widths of crossings in Poisson Boolean percolation

Ioan Manolescu·Leonardo V. Santoro
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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 $n\times n$ 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.

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Ioan Manolescu, Leonardo V. Santoro. 2022-11-21. Widths of crossings in Poisson Boolean percolation. https://doi.org/10.1017/jpr.2024.91

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