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Record statistics and persistence for a random walk with a drift

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  • Satya N. Majumdar
  • Gregory Schehr
  • Gregor Wergen
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    Abstract

    We study the statistics of records of a one-dimensional random walk of n steps, starting from the origin, and in presence of a constant bias c. At each time-step the walker makes a random jump of length \eta drawn from a continuous distribution f(\eta) which is symmetric around a constant drift c. We focus in particular on the case were f(\eta) is a symmetric stable law with a L\'evy index 0

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    File URL: http://arxiv.org/pdf/1206.6972
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1206.6972.

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    Date of creation: Jun 2012
    Date of revision: Aug 2012
    Publication status: Published in J. Phys. A: Math. Theor. 45 (2012) 355002
    Handle: RePEc:arx:papers:1206.6972

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    Web page: http://arxiv.org/

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    Cited by:
    1. Gregory Schehr & Satya N. Majumdar, 2013. "Exact record and order statistics of random walks via first-passage ideas," Papers 1305.0639, arXiv.org.

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