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On self-repellent one dimensional random walks
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  • Published: December 1990

On self-repellent one dimensional random walks

  • Erwin Bolthausen1 nAff2 

Probability Theory and Related Fields volume 86, pages 423–441 (1990)Cite this article

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  • 14 Citations

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Summary

We consider an ordinary one dimensional recurrent random walk onℤ. A self-repellent random walk is defined by changing the ordinary law of the random walk in the following way: A path gets a new relative weight by multiplying the old one with a factor 1−λ for every self intersection of the path. 0<λ<1 is a parameter.

It is shown that if the jump distribution of the random walk has an exponential moment and if λ is small enough then the displacement of the endpoint is asymptotically of the order of the length of the path.

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References

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Author information

Author notes
  1. Erwin Bolthausen

    Present address: Institut für Angewandte Mathematik der Universität, Rämistrasse 74, CH-8001, Zürich, Switzerland

Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Berlin, Strasse des 17. Juni 136, D-1000, Berlin 12, Germany

    Erwin Bolthausen

Authors
  1. Erwin Bolthausen
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Additional information

Partially supported by the Deutsche Forschungsgemeinschaft and the Akademie der Wissenschaften zu Berlin

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Cite this article

Bolthausen, E. On self-repellent one dimensional random walks. Probab. Th. Rel. Fields 86, 423–441 (1990). https://doi.org/10.1007/BF01198167

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  • Received: 25 May 1989

  • Revised: 26 March 1990

  • Issue Date: December 1990

  • DOI: https://doi.org/10.1007/BF01198167

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Keywords

  • Endpoint
  • Stochastic Process
  • Random Walk
  • Probability Theory
  • Mathematical Biology
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