Entropy (Dec 2020)

A Continuous-Time Random Walk Extension of the Gillis Model

  • Gaia Pozzoli,
  • Mattia Radice,
  • Manuele Onofri,
  • Roberto Artuso

DOI
https://doi.org/10.3390/e22121431
Journal volume & issue
Vol. 22, no. 12
p. 1431

Abstract

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We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional non-homogeneous random walk with a position-dependent drift known in the mathematical literature as Gillis random walk. This modified stochastic process allows to significantly change local, non-local and transport properties in the presence of heavy-tailed waiting-time distributions lacking the first moment: we provide here exact results concerning hitting times, first-time events, survival probabilities, occupation times, the moments spectrum and the statistics of records. Specifically, normal diffusion gives way to subdiffusion and we are witnessing the breaking of ergodicity. Furthermore we also test our theoretical predictions with numerical simulations.

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