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Self-intersections of 1-dimensional random walks
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  • Published: July 1986

Self-intersections of 1-dimensional random walks

  • David J. Aldous1 

Probability Theory and Related Fields volume 72, pages 559–587 (1986)Cite this article

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Summary

Consider a random walk S n on the integers, where the steps ξ i have mean 0 and variance σ2. Let T be the time of first self-intersection of the random walk. It is shown that, as σ→∞, T grows at rate σ2/3. More precisely, Tσ2/3 has a non-degenerate limit distribution which can be described in terms of Brownian motion local time.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of California, 94720, Berkeley, CA, USA

    David J. Aldous

Authors
  1. David J. Aldous
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Additional information

Research supported by National Science Foundation Grant MCS80-02698.

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Aldous, D.J. Self-intersections of 1-dimensional random walks. Probab. Th. Rel. Fields 72, 559–587 (1986). https://doi.org/10.1007/BF00344721

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  • Received: 07 March 1985

  • Issue Date: July 1986

  • DOI: https://doi.org/10.1007/BF00344721

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Keywords

  • Stochastic Process
  • Brownian Motion
  • Random Walk
  • Probability Theory
  • Statistical Theory
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