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.

Pozzoli, G., Radice, M., Onofri, M., Artuso, R. (2020). A Continuous-Time Random Walk Extension of the Gillis Model. ENTROPY, 22(12), 1-29 [10.3390/e22121431].

A Continuous-Time Random Walk Extension of the Gillis Model

Pozzoli, G;
2020

Abstract

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.
Articolo in rivista - Articolo scientifico
Anomalous diffusion; Biased processes; CTRW; Ergodicity; First-time events; Gillis model;
English
2020
22
12
1
29
1431
none
Pozzoli, G., Radice, M., Onofri, M., Artuso, R. (2020). A Continuous-Time Random Walk Extension of the Gillis Model. ENTROPY, 22(12), 1-29 [10.3390/e22121431].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/469182
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