Permanent URL to this publication: http://dx.doi.org/10.5167/uzh21826
van den Berg, M; Bolthausen, E; den Hollander, F (2004). On the volume of the intersection of two Wiener sausages. Annals of Mathematics. Second Series, 159(2):741782.

PDF
1MB 
Abstract
For , let be the neighbourhoods of the th copy of a standard Brownian motion in starting at 0, until time . The authors prove large deviations results about , for , and suggest extensions applicable to , the volume of the intersection of sausages.
In particular, for , I_d^(c)t (here is the Newtonian capacity of the ball of radius ). A similar result holds for with replaced by and replaced by . The sizes of the large deviations come from the asymptotic value of the expected volume of a single Wiener sausage. A variational representation is derived for , and the authors also investigate the dependence of on for different values of .
The work is motivated by the desire to address a number of open problems arising in the discrete setting from the study of the tail of the distribution of the intersection of the ranges of two independent random walks in (in such cases no exact rate constant is known).
The results in the paper draw on ideas and techniques developed by the authors to handle large deviations for the volume of a single Wiener sausage.
Item Type:  Journal Article, refereed, original work 

Communities & Collections:  07 Faculty of Science > Institute of Mathematics 
DDC:  510 Mathematics 
Uncontrolled Keywords:  Wiener sausages, intersection volume, large deviations, variational problems, Sobolev inequalities. 
Language:  English 
Date:  2004 
Deposited On:  21 Apr 2010 13:15 
Last Modified:  28 Nov 2013 00:34 
Publisher:  Mathematical Sciences Publishers 
ISSN:  0003486X 
Official URL:  http://annals.math.princeton.edu/annals/2004/1592/p06.xhtml 
Citations:  Web of Science®. Times Cited: 5 Google Scholar™ Scopus®. Citation Count: 5 
Users (please log in): suggest update or correction for this item
Repository Staff Only: item control page