Replica overlap and covering time for the Wiener sausages among Poissonian obstacles (Q1012034)

The author studies two problems concerning the Wiener sausage among Poissonian obstacles. The first result is that the intersection of two independent Wiener sausages is asymptotically equal to their union. Besides the asymptotics for the volume, it is possible to determine the shape. It is a consequence of the theorem that states confinement property of two particles. The second problem is to estimate the covering time of the confinement ball by the single Wiener sausage. It is proved that the time needed to fill the confinement ball has the same order as its volume.