Strong law of large numbers for the capacity of the Wiener sausage in dimension four

TL;DR

This paper establishes a strong law of large numbers for the Newtonian capacity of Wiener sausages specifically in four-dimensional space, addressing a critical case in stochastic analysis.

Contribution

It provides the first rigorous proof of a strong law of large numbers for Wiener sausage capacity in the critical dimension four.

Findings

Proves a strong law of large numbers for Wiener sausage capacity in dimension four

Addresses the critical case in stochastic potential theory

Advances understanding of Wiener sausage properties in high dimensions

Abstract

We prove a strong law of large numbers for the Newtonian capacity of a Wiener sausage in the critical dimension four.