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The drift of a one-dimensional self-avoiding random walk
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  • Published: December 1993

The drift of a one-dimensional self-avoiding random walk

  • Wolfgang König1 

Probability Theory and Related Fields volume 96, pages 521–543 (1993)Cite this article

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Summary

We prove that a self-avoiding random walk on the integers with bounded increments grows linearly. We characterize its drift in terms of the Frobenius eigenvalue of a certain one parameter family of primitive matrices. As an important tool, we express the local times as a two-block functional of a certain Markov chain, which is of independent interest.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Zürich, Rämistrasse 74, CH-8001, Zürich, Switzerland

    Wolfgang König

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  1. Wolfgang König
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Cite this article

König, W. The drift of a one-dimensional self-avoiding random walk. Probab. Th. Rel. Fields 96, 521–543 (1993). https://doi.org/10.1007/BF01200208

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  • Received: 18 December 1992

  • Revised: 21 April 1993

  • Issue Date: December 1993

  • DOI: https://doi.org/10.1007/BF01200208

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Mathematics Subject Classification (1980)

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