ISSN:
1432-2064
Keywords:
60K35
;
58E30
;
60F10
;
60J15
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary Consider a one-dimensional walk (S k ) k having steps of bounded size, and weight the probability of the path with some factor 1−α∈(0,1) for every single self-intersection up to timen. We prove thatS n /S S converges towards some deterministic number called the effective drift of the self-repellent walk. Furthermore, this drift is shown to tend to the basic drift as α tends to 0 and, as α tends to 1, to the self-avoiding walk's drift which is introduced in [10]. The main tool of the present paper is a representation of the sequence of the local times as a functional of a certain Markov process.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01268992
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