Asymptotics for the Wiener sausage among Poissonian obstacles

Details Asymptotics for the Wiener sausage among Poissonian obstacles Asymptotics for the Wiener sausage among Poissonian obstacles

2007-09-12

arxiv.org/abs/0709.1751v2

Journal of Statistical Physics 2008, Vol. 133 No 4, 639-657

Mathematics

Probability

19 pages, Major revision made for publication in J. Stat. Phys

Scientific paper

10.1007/s10955-008-9629-5

We consider the Wiener sausage among Poissonian obstacles. The obstacle is called hard if Brownian motion entering the obstacle is immediately killed, and is called soft if it is killed at certain rate. It is known that Brownian motion conditioned to survive among obstacles is confined in a ball near its starting point. We show the weak law of large numbers, large deviation principle in special cases and the moment asymptotics for the volume of the corresponding Wiener sausage. One of the consequence of our results is that the trajectory of Brownian motion almost fills the confinement ball.

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