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

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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.

Keywords

Capacity Wiener sausage Law of large numbers 

Mathematics Subject Classification

Primary 60F05 60G50 

Notes

Acknowledgements

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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Université Paris-Est CréteilCréteilFrance
  2. 2.CNRS, Centrale Marseille, I2M, UMR 7373Aix-Marseille UniversitéMarseilleFrance
  3. 3.University of CambridgeCambridgeUK

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