Year: 2026
Type: preprint
Abstract: For a finite set $A\subseteq\mathbb Z^d$, we study the capacities of a sausage obtained by transporting $A$ along the Minkowski sum of simple or critical branching random walks. We first establish quantitative capacity estimates for the random walk sausage and the branching sausage. This in turn, gives us estimates for the probability that Minkowski sums of a mixture of walks hit a finite set in high dimensions. Our approach is based on an annular decomposition of a critical branching random walk into successive waves, which may have further applications.
Source: arXiv (Cornell University)
Author: Ishak, Joelle
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221095492