Minkowski sum of fractal percolation and random sets

Abstract

In this paper, we prove that hitting probability of Minkowski sum of fractal percolations can be characterized by capacity. Then we extend this result to Minkowski sum of general random sets in ${\mathbb{Z}}^d$, including ranges of random walks and critical branching random walks, whose hitting probabilities are described by Newtonian capacity individually.

24 pages, 7 figures

References in corpus (2)

• Intersections of branching random walks on ${\mathbb{Z}}^8$
• Branching random walks and Minkowski sum of random walks