Abstract
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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We warmly thank the referee for his/her very careful reading and insightful comments, which greatly helped improve, clarify and correct the paper.
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Asselah, A., Schapira, B. & Sousi, P. Strong law of large numbers for the capacity of the Wiener sausage in dimension four. Probab. Theory Relat. Fields 173, 813–858 (2019). https://doi.org/10.1007/s00440-018-0842-0
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DOI: https://doi.org/10.1007/s00440-018-0842-0
Keywords
- Capacity
- Wiener sausage
- Law of large numbers
Mathematics Subject Classification
- Primary 60F05
- 60G50