Widths of crossings in Poisson Boolean percolation

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.

References in corpus (2)

• Fluctuation theory of connectivities for subcritical random cluster models
• Planar random-cluster model: fractal properties of the critical phase