Strong law of large numbers for the capacity of the Wiener sausage in dimension four
Résumé
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 requires a delicate analysis of intersection probabilities between two independent Wiener sausages.
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