Quenched Invariance Principle for a Reflecting Diffusion in a Continuum Percolation Cluster

TL;DR

This paper proves a quenched invariance principle for reflecting diffusions on a percolation cluster in a continuum, under certain regularity and ergodicity assumptions, advancing understanding of stochastic processes in random media.

Contribution

It establishes a quenched invariance principle for reflecting diffusions in continuum percolation clusters with volume regularity and isoperimetric conditions, a novel result in stochastic homogenization.

Findings

Proves quenched invariance principle for reflecting diffusions

Validates assumptions on volume regularity and isoperimetric conditions

Extends stochastic homogenization to continuum percolation clusters

Abstract

We consider a continuum percolation built over stationary ergodic point processes. Assuming that the occupied region has a unique unbounded cluster and the cluster satisfies volume regularity and isoperimetric condition, we prove a quenched invariance principle for reflecting diffusions on the cluster.