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Large deviations estimates for self-intersection local times for simple random walk in \({\mathbb{Z}}^3\)
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  • Published: 16 June 2007

Large deviations estimates for self-intersection local times for simple random walk in \({\mathbb{Z}}^3\)

  • Amine Asselah1 

Probability Theory and Related Fields volume 141, pages 19–45 (2008)Cite this article

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Abstract

We obtain large deviations estimates for the self-intersection local times for a simple random walk in dimension 3. Also, we show that the main contribution to making the self-intersection large, in a time period of length n, comes from sites visited less than some power of log(n). This is opposite to the situation in dimensions larger or equal to 5. Finally, we present an application of our estimates to moderate deviations for random walk in random sceneries.

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Authors and Affiliations

  1. LAMA, Université de Paris, XII. Av. du General de Gaulle, 94010, Creteil, Cedex, France

    Amine Asselah

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  1. Amine Asselah
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Correspondence to Amine Asselah.

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Asselah, A. Large deviations estimates for self-intersection local times for simple random walk in \({\mathbb{Z}}^3\) . Probab. Theory Relat. Fields 141, 19–45 (2008). https://doi.org/10.1007/s00440-007-0078-x

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  • Received: 12 April 2006

  • Revised: 16 April 2007

  • Published: 16 June 2007

  • Issue Date: May 2008

  • DOI: https://doi.org/10.1007/s00440-007-0078-x

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Keywords

  • Self-intersection local times
  • Random walk
  • Random sceneries

Mathematics Subject Classification (2000)

  • 60K35
  • 82C22
  • 60J25
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