“Phase transitions and large deviations for the Boolean model of continuum percolation for Cox point processes”
Venerdì 25 Marzo 2022, ore 14:30 - Zoom - Benedikt Jahnel (WIAS, Berlin, Germany)
In this talk, I consider the Boolean model with random radii based on Cox point processes, i.e., Poisson point processes in a random environment. Under a condition of stabilization for the random environment, our results establish existence and non-existence of subcritical regimes for the size of the cluster at the origin in terms of volume, diameter and number of points, also including their moments. The second part of the talk will address rates of convergence of the percolation probability for the Cox-Boolean model with fixed radii in a variety of asymptotic regimes.
This is based on joint work with Christian Hirsch, András Tóbiás and Élie Cali.