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A note on the critical dimension for weakly self-avoiding walks
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  • Published: September 1988

A note on the critical dimension for weakly self-avoiding walks

  • Wei-Shih Yang1 &
  • D. Klein2 

Probability Theory and Related Fields volume 79, pages 99–114 (1988)Cite this article

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  • 7 Citations

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Summary

We consider a weakly self-avoiding T-step random walk on Z dwith possible nonnearest neighbor jumps. We prove that for d≧3, the scaling limit of the end point is Cauchy distributed as T→∞.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Minnesota, 55455, Minneapolis, MN, USA

    Wei-Shih Yang

  2. Department of Mathematics, California State University, 91330, Northridge, California, USA

    D. Klein

Authors
  1. Wei-Shih Yang
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  2. D. Klein
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Additional information

Partially supported by NSF grant DMS 8702558

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Cite this article

Yang, WS., Klein, D. A note on the critical dimension for weakly self-avoiding walks. Probab. Th. Rel. Fields 79, 99–114 (1988). https://doi.org/10.1007/BF00319107

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  • Received: 02 January 1988

  • Revised: 29 March 1988

  • Issue Date: September 1988

  • DOI: https://doi.org/10.1007/BF00319107

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Keywords

  • Stochastic Process
  • Random Walk
  • Probability Theory
  • Statistical Theory
  • Critical Dimension
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