Journal of Mathematics of Kyoto University

Replica overlap and covering time for the Wiener sausages among Poissonian obstacles

Fukushima, Ryoki

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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.

Article information

Source
J. Math. Kyoto Univ., Volume 48, Number 2 (2008), 455-470.

Dates
First available in Project Euclid: 14 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250271422

Digital Object Identifier
doi:10.1215/kjm/1250271422

Mathematical Reviews number (MathSciNet)
MR2436747

Zentralblatt MATH identifier
1186.60081

Citation

Fukushima, Ryoki. Replica overlap and covering time for the Wiener sausages among Poissonian obstacles. J. Math. Kyoto Univ. 48 (2008), no. 2, 455--470. doi:10.1215/kjm/1250271422. https://projecteuclid.org/euclid.kjm/1250271422


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