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Continuous time persistent random walk: a review and some generalizations

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Abstract

We review some extensions of the continuous time random walk first introduced by Elliott Montroll and George Weiss more than 50 years ago [E.W. Montroll, G.H. Weiss, J. Math. Phys. 6, 167 (1965)], extensions that embrace multistate walks and, in particular, the persistent random walk. We generalize these extensions to include fractional random walks and derive the associated master equation, namely, the fractional telegrapher’s equation. We dedicate this review to our joint work with George H. Weiss (1930–2017). It saddens us greatly to report the recent death of George Weiss, a scientific giant and at the same time a lovely and humble man.

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Authors and Affiliations

  1. Department of Condensed Matter Physics and Complex Systems Institute (UBICS), University of Barcelona, Catalonia, Spain

    Jaume Masoliver

  2. Department of Chemistry and Biochemistry and BioCircuits Institute, University of California, San Diego, USA

    Katja Lindenberg

Authors
  1. Jaume Masoliver
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  2. Katja Lindenberg
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Correspondence to Jaume Masoliver.

Additional information

Contribution to the Topical Issue: “Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook”, edited by Ryszard Kutner and Jaume Masoliver.

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Masoliver, J., Lindenberg, K. Continuous time persistent random walk: a review and some generalizations. Eur. Phys. J. B 90, 107 (2017). https://doi.org/10.1140/epjb/e2017-80123-7

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  • DOI: https://doi.org/10.1140/epjb/e2017-80123-7

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