Large time volume of the pinned Wiener sausage to second order

✍ Scribed by I. McGillivray

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 244 KB
• Volume: 284
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200910460

✦ Synopsis

Abstract

We investigate the large time behaviour of the expected volume of the pinned Wiener sausage associated to a compact subset K in \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ {\mathbb R}^d $\end{document} for d ⩾ 3. The structure of the asymptotic series is known: it depends strongly on whether the dimension d is odd or even; and the leading coefficient is given by the Newtonian capacity of K. In this article, we obtain detailed expressions for the second order coefficients. It is noteworthy that these coefficients feature novel potential‐theoretic terms that do not appear in the unpinned case. The proof exploits a trace formula of Krein. In the course of the argument, we derive a low‐energy expansion to second order for the Krein spectral shift function for an obstacle scattering system. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim