# Replica overlap and covering time for the Wiener sausages among Poissonian obstacles - Mathematics > Probability

Abstract: We study two objects concerning the Wiener sausage among Poissonianobstacles. The first is the asymptotics for the \textit{replica overlap}, whichis the intersection of two independent Wiener sausages. We show that it isasymptotically equal to their union. This result confirms that the localizingeffect of the media is so strong as to completely determine the motional rangeof particles. The second is an estimate on the \textit{covering time}. It isknown that the Wiener sausage avoiding Poissonian obstacles up to time $t$ isconfined in some `clearing- ball near the origin and almost fills it. We provehere that the time needed to fill the confinement ball has the same order asits volume.

Author: Ryoki Fukushima

Source: https://arxiv.org/