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Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-22578

Bolthausen, E; Schmock, U (1995). On self-attracting random walks. In: Cranston, M C; Pinsky, M A. Stochastic analysis (Ithaca, NY, 1993). Providence, RI, 23-44. ISBN 0-8218-0289-5.

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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 continuous-time, symmetric, nearest-neighbour 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 self-attracting
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
DDC:510 Mathematics
Uncontrolled Keywords:nearest-neighbor random walk; self-attracting 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:0082-0717
ISBN:0-8218-0289-5
Additional Information:First published in [On self-attracting random walks. Stochastic analysis (Ithaca, NY, 1993), 23--44, Proc. Sympos. Pure Math., 57], published by the American Mathematical Society
Official URL:http://www.ams.org/bookstore?fn=20&arg1=pspumseries&ikey=PSPUM-57
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0829.60021
http://www.fam.tuwien.ac.at/~schmock/Attracting_walks.html

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