Homogenization of a reflecting barrier Brownian motion in a continuum percolation cluster in \(R^ d\)
A continuum percolation model in \(\mathbb{R}^ d\) \((d \geq 2)\), which is called the Poisson blob model, is considered. It should be viewed as a continuum analogue of the discrete site percolation model. Instead of sites being independently occupied we have a Poisson process with each Poisson point being the center of an occupied disc of radius \(r\). A central limit theorem is proven for a reflecting Brownian motion in an unbounded occupied cluster of the model in the supercritical case. For an unbounded vacant cluster of the model, a similar result is obtained in the subcritical case.
scientific article; zbMATH DE number 701566
scientific article