Strong law of large numbers for the capacity of the Wiener sausage in dimension four
Probability Theory and Related Fields
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Asselah, A., Schapira, B., & Sousi, P. (2019). Strong law of large numbers for the capacity of the Wiener sausage in dimension four. Probability Theory and Related Fields, 173 (3-4), 813-858. https://doi.org/10.1007/s00440-018-0842-0
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.
External DOI: https://doi.org/10.1007/s00440-018-0842-0
This record's URL: https://www.repository.cam.ac.uk/handle/1810/277053