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Multi-excited random walks on integers
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  • Published: 03 May 2005

Multi-excited random walks on integers

  • Martin P.W. Zerner1 

Probability Theory and Related Fields volume 133, pages 98–122 (2005)Cite this article

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  • 59 Citations

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Abstract

We introduce a class of nearest-neighbor integer random walks in random and non-random media, which includes excited random walks considered in the literature. At each site the random walker has a drift to the right, the strength of which depends on the environment at that site and on how often the walker has visited that site before. We give exact criteria for recurrence and transience and consider the speed of the walk.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany

    Martin P.W. Zerner

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  1. Martin P.W. Zerner
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Corresponding author

Correspondence to Martin P.W. Zerner.

Additional information

Most of this work was done while the author was Szegö Assistant Professor at Stanford University.

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Cite this article

Zerner, M. Multi-excited random walks on integers. Probab. Theory Relat. Fields 133, 98–122 (2005). https://doi.org/10.1007/s00440-004-0417-0

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  • Received: 05 March 2004

  • Revised: 23 November 2004

  • Published: 03 May 2005

  • Issue Date: September 2005

  • DOI: https://doi.org/10.1007/s00440-004-0417-0

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Mathematics Subject Classification (2000):

  • 60K35
  • 60K37
  • 60J10

Key words or phrases

  • Excited Random Walk
  • Law of Large Numbers
  • Perturbed Random Walk
  • Recurrence
  • Self-Interacting Random Walk
  • Transience
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