Large-N Limit of Crossing Probabilities, Discontinuity, and Asymptotic Behavior of Threshold Values in Mandelbrot's Fractal Percolation Process

Erik I. Broman, Federico Camia

We study Mandelbrot's percolation process in dimension $d\ge 2$. The process generates random fractal sets by an iterative procedure which starts by dividing the unit cube $[0,1]…