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Mathematics > Probability

arXiv:0709.1751 (math)
[Submitted on 12 Sep 2007 (v1), last revised 18 Nov 2008 (this version, v2)]

Title:Asymptotics for the Wiener sausage among Poissonian obstacles

Authors:Ryoki Fukushima
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Abstract: 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.
Comments: 19 pages, Major revision made for publication in J. Stat. Phys
Subjects: Probability (math.PR); Mathematical Physics (math-ph)
MSC classes: 60K37; 60G17; 82D30
Cite as: arXiv:0709.1751 [math.PR]
  (or arXiv:0709.1751v2 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.0709.1751
Journal reference: Journal of Statistical Physics 2008, Vol. 133 No 4, 639-657
Related DOI: https://doi.org/10.1007/s10955-008-9629-5

Submission history

From: Ryoki Fukushima [view email]
[v1] Wed, 12 Sep 2007 04:49:19 UTC (15 KB)
[v2] Tue, 18 Nov 2008 16:01:21 UTC (16 KB)
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