Translator Disclaimer
2008 Replica overlap and covering time for the Wiener sausages among Poissonian obstacles
Ryoki Fukushima
J. Math. Kyoto Univ. 48(2): 455-470 (2008). DOI: 10.1215/kjm/1250271422

Abstract

We study two objects concerning the Wiener sausage among Poissonian obstacles. The first is the asymptotics for the \emph{replica overlap}, which is the intersection of two independent Wiener sausages. We show that it is asymptotically equal to their union. This result confirms that the localizing effect of the media is so strong as to completely determine the motional range of particles. The second is an estimate on the \emph{covering time}. It is known that the Wiener sausage avoiding Poissonian obstacles up to time t is confined in some \lq clearing \rq ball near the origin and almost fills it. We prove here that the time needed to fill the confinement ball has the same order as its volume.

Citation

Download Citation

Ryoki Fukushima. "Replica overlap and covering time for the Wiener sausages among Poissonian obstacles." J. Math. Kyoto Univ. 48 (2) 455 - 470, 2008. https://doi.org/10.1215/kjm/1250271422

Information

Published: 2008
First available in Project Euclid: 14 August 2009

zbMATH: 1186.60081
MathSciNet: MR2436747
Digital Object Identifier: 10.1215/kjm/1250271422

Rights: Copyright © 2008 Kyoto University

JOURNAL ARTICLE
16 PAGES


SHARE
Vol.48 • No. 2 • 2008
Back to Top