Lévy flights versus Lévy walks in bounded domains

Bartłomiej Dybiec, Ewa Gudowska-Nowak, Eli Barkai, Alexander A. Dubkov

Research output: Contribution to journalArticlepeer-review

Abstract

Lévy flights and Lévy walks serve as two paradigms of random walks resembling common features but also bearing fundamental differences. One of the main dissimilarities is the discontinuity versus continuity of their trajectories and infinite versus finite propagation velocity. As a consequence, a well-developed theory of Lévy flights is associated with their pathological physical properties, which in turn are resolved by the concept of Lévy walks. Here, we explore Lévy flight and Lévy walk models on bounded domains, examining their differences and analogies. We investigate analytically and numerically whether and under which conditions both approaches yield similar results in terms of selected statistical observables characterizing the motion: the survival probability, mean first passage time, and stationary probability density functions. It is demonstrated that the similarity of the models is affected by the type of boundary conditions and the value of the stability index defining the asymptotics of the jump length distribution.

Original languageEnglish
Article number052102
JournalPhysical Review E
Volume95
Issue number5
DOIs
StatePublished - 3 May 2017

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

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