Universal Behavior of Connectivity Properties in Fractal Percolation Models
Universal Behavior of Connectivity Properties in Fractal Percolation Models
Partially motivated by the desire to better understand the connectivity phase transition in fractal percolation, we introduce and study a class of continuum fractal percolation models in dimension $d\geq2$. These include a scale invariant version of the classical (Poisson) Boolean model of stochastic geometry and (for $d=2$) the Brownian loop …