## Journal of Mathematics of Kyoto University

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

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

#### 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