Large time volume of the pinneds Wiener sausage to second order

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)

Abstract

We investigate the large time behaviour of the expected volume of the pinned Wiener sausage associated to a compact subset K in 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.
Translated title of the contributionLarge time volume of the pinneds Wiener sausage to second order
Original languageEnglish
Pages (from-to)142 - 165
Number of pages24
JournalMathematische Nachrichten
Volume284, issue 2-3
DOIs
Publication statusPublished - Mar 2011

Bibliographical note

Publisher: Wiley

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