Cargando…
A Continuous-Time Random Walk Extension of the Gillis Model
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 pro...
Autores principales: | , , , |
---|---|
Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2020
|
Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7766702/ https://www.ncbi.nlm.nih.gov/pubmed/33353053 http://dx.doi.org/10.3390/e22121431 |
_version_ | 1783628781598015488 |
---|---|
author | Pozzoli, Gaia Radice, Mattia Onofri, Manuele Artuso, Roberto |
author_facet | Pozzoli, Gaia Radice, Mattia Onofri, Manuele Artuso, Roberto |
author_sort | Pozzoli, Gaia |
collection | PubMed |
description | 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. |
format | Online Article Text |
id | pubmed-7766702 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-77667022021-02-24 A Continuous-Time Random Walk Extension of the Gillis Model Pozzoli, Gaia Radice, Mattia Onofri, Manuele Artuso, Roberto Entropy (Basel) Article 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. MDPI 2020-12-18 /pmc/articles/PMC7766702/ /pubmed/33353053 http://dx.doi.org/10.3390/e22121431 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Pozzoli, Gaia Radice, Mattia Onofri, Manuele Artuso, Roberto A Continuous-Time Random Walk Extension of the Gillis Model |
title | A Continuous-Time Random Walk Extension of the Gillis Model |
title_full | A Continuous-Time Random Walk Extension of the Gillis Model |
title_fullStr | A Continuous-Time Random Walk Extension of the Gillis Model |
title_full_unstemmed | A Continuous-Time Random Walk Extension of the Gillis Model |
title_short | A Continuous-Time Random Walk Extension of the Gillis Model |
title_sort | continuous-time random walk extension of the gillis model |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7766702/ https://www.ncbi.nlm.nih.gov/pubmed/33353053 http://dx.doi.org/10.3390/e22121431 |
work_keys_str_mv | AT pozzoligaia acontinuoustimerandomwalkextensionofthegillismodel AT radicemattia acontinuoustimerandomwalkextensionofthegillismodel AT onofrimanuele acontinuoustimerandomwalkextensionofthegillismodel AT artusoroberto acontinuoustimerandomwalkextensionofthegillismodel AT pozzoligaia continuoustimerandomwalkextensionofthegillismodel AT radicemattia continuoustimerandomwalkextensionofthegillismodel AT onofrimanuele continuoustimerandomwalkextensionofthegillismodel AT artusoroberto continuoustimerandomwalkextensionofthegillismodel |