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

14 Jun 2018

We prove a strong law of large numbers for the Newtonian capacity of a Wiener sausage in the critical dimension four, where a logarithmic correction appears in the scaling. The main step of the proof is to obtain precise asymptotics for the expected value of the capacity. This re- quires a delicate analysis of intersection probabilities between two independent Wiener sausages.