Permanent URL to this publication: http://dx.doi.org/10.5167/uzh22578
Bolthausen, E; Schmock, U (1995). On selfattracting random walks. In: Cranston, M C; Pinsky, M A. Stochastic analysis (Ithaca, NY, 1993). Providence, RI, 2344. ISBN 0821802895.

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Abstract
In this survey paper we mainly discuss the results contained in two of our recent articles [2] and [5]. Let {Xt}t≥0 be a continuoustime, symmetric, nearestneighbour random walk on Zd. For every T > 0 we define the transformed path measure dPT = (1/ZT ) exp(HT ) dP, where P is the original one and ZT is the appropriate normalizing constant. The Hamiltonian HT imparts the selfattracting interaction of the paths up to time T. We consider the case where HT is given by a potential function V on Zd with finite support, and the case HT = −NT , where NT denotes the number of points visited by the random walk up to time T. In both cases the typical paths under PT as T →∞ clump together much more than those of the free random walk and give rise to localization phenomena.
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Additional indexing
Item Type:  Book Section, refereed, original work 

Communities & Collections:  07 Faculty of Science > Institute of Mathematics 
Dewey Decimal Classification:  510 Mathematics 
Uncontrolled Keywords:  nearestneighbor random walk; selfattracting interaction; localization phenomena 
Language:  English 
Date:  1995 
Deposited On:  20 May 2010 12:53 
Last Modified:  09 Jul 2012 03:57 
Publisher:  American Mathematical Society 
Series Name:  Proceedings of Symposia in Pure Mathematics 
Number:  57 
ISSN:  00820717 
ISBN:  0821802895 
Additional Information:  First published in [On selfattracting random walks. Stochastic analysis (Ithaca, NY, 1993), 2344, Proc. Sympos. Pure Math., 57], published by the American Mathematical Society 
Official URL:  http://www.ams.org/bookstore?fn=20&arg1=pspumseries&ikey=PSPUM57 
Related URLs:  http://www.zentralblattmath.org/zbmath/search/?q=an%3A0829.60021 http://www.fam.tuwien.ac.at/~schmock/Attracting_walks.html 
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