Continuous time persistent random walk: a review and some generalizations

Regular Article
Part of the following topical collections:
  1. Topical issue: Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook

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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Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Condensed Matter Physics and Complex Systems Institute (UBICS)University of BarcelonaCataloniaSpain
  2. 2.Department of Chemistry and Biochemistry and BioCircuits InstituteUniversity of CaliforniaSan DiegoUSA

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