Tuesday, December 11, 2007

The Wiener Sausage

I was just introduced by my roommate to the mathematical Wiener sausage. My first introduction came from this 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.

I had trouble believing that this could be real, but it's very real indeed. In fact, it turns out that there's a Wiener measure.

Because I have the sense of humor of a 12-year old, I was dying to learn more. A quick search of Google Scholar yielded some great titles (links provided to prove that I'm not making this up):
Read any other good scholarly articles on the Wiener sausage lately?


Excimer said...

The obstacle is called hard

and that was as far as I got.

Ψ*Ψ said...