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Excited random walk against a wall
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  • Published: 15 February 2007

Excited random walk against a wall

  • Gideon Amir1,
  • Itai Benjamini1 &
  • Gady Kozma1 

Probability Theory and Related Fields volume 140, pages 83–102 (2008)Cite this article

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  • 8 Citations

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Abstract

We analyze random walk in the upper half of a three-dimensional lattice which goes down whenever it encounters a new vertex, a.k.a. excited random walk. We show that it is recurrent with an expected number of returns of \(\sqrt{\log t}\).

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Authors and Affiliations

  1. Weizmann Institute, Rehovot, 76100, Israel

    Gideon Amir, Itai Benjamini & Gady Kozma

Authors
  1. Gideon Amir
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  2. Itai Benjamini
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  3. Gady Kozma
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Correspondence to Gady Kozma.

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Cite this article

Amir, G., Benjamini, I. & Kozma, G. Excited random walk against a wall. Probab. Theory Relat. Fields 140, 83–102 (2008). https://doi.org/10.1007/s00440-007-0058-1

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  • Received: 26 October 2005

  • Revised: 27 October 2006

  • Published: 15 February 2007

  • Issue Date: January 2008

  • DOI: https://doi.org/10.1007/s00440-007-0058-1

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Keywords

  • Random Walk
  • Half Space
  • Simple Random Walk
  • Heuristic Argument
  • Geometric Random Variable
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