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The drift of a one-dimensional self-repellent random walk with bounded increments
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  • Published: December 1994

The drift of a one-dimensional self-repellent random walk with bounded increments

  • Wolfgang König1 

Probability Theory and Related Fields volume 100, pages 513–544 (1994)Cite this article

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  • 6 Citations

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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.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik der Universität Zürich-Irchel, Winterthurerstrasse 190, CH-8057, Zürich, Switzerland

    Wolfgang König

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  1. Wolfgang König
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Additional information

Partially supported by Swiss National Sciences Foundation Grant 20-36305.92

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König, W. The drift of a one-dimensional self-repellent random walk with bounded increments. Probab. Th. Rel. Fields 100, 513–544 (1994). https://doi.org/10.1007/BF01268992

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  • Received: 07 May 1993

  • Revised: 25 May 1994

  • Issue Date: December 1994

  • DOI: https://doi.org/10.1007/BF01268992

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Mathematics Subject Classfication (1991)

  • 60K35
  • 58E30
  • 60F10
  • 60J15
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