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.
In this survey paper we mainly discuss the results contained in two of our recent articles  and . Let 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.
|Item Type:||Book Section, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Uncontrolled Keywords:||nearest-neighbor random walk; self-attracting interaction; localization phenomena|
|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|
|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|
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