On the relevance of q-distribution functions: The return time distribution of restricted random walker

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dc.contributor.authorZand J.
dc.contributor.authorTirnakli U.
dc.contributor.authorJensen H.J.
dc.date.accessioned2019-10-26T21:21:19Z
dc.date.available2019-10-26T21:21:19Z
dc.date.issued2015
dc.departmentEge Üniversitesien_US
dc.description.abstractThere exists a large literature on the application of q-statistics to the out-of-equilibrium non-ergodic systems in which some degree of strong correlations exists. Here we study the distribution of first return times to zero, PR (0, t), of a random walk on the set of integers {0, 1, 2,..., L} with a position dependent transition probability given by . We find that for all values of PR(0, t) can be fitted by q-exponentials, but only for a = 1 is PR (0, t) given exactly by a q-exponential in the limit . This is a remarkable result since the exact analytical solution of the corresponding continuum model represents PR (0, t) as a sum of Bessel functions with a smooth dependence on a from which we are unable to identify a = 1 as of special significance. However, from the high precision numerical iteration of the discrete master equation, we do verify that only for a = 1 is PR(0, t) exactly a q-exponential and that a tiny departure from this parameter value makes the distribution deviate from q-exponential. Further research is certainly required to identify the reason for this result and also the applicability of q-statistics and its domain. � 2015 IOP Publishing Ltd.en_US
dc.identifier.doi10.1088/1751-8113/48/42/425004
dc.identifier.issn1751-8113
dc.identifier.issn1751-8113en_US
dc.identifier.issue42en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.urihttps://doi.org/10.1088/1751-8113/48/42/425004
dc.identifier.urihttps://hdl.handle.net/11454/16859
dc.identifier.volume48en_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherInstitute of Physics Publishingen_US
dc.relation.ispartofJournal of Physics A: Mathematical and Theoreticalen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectq-statisticsen_US
dc.subjectrandom walksen_US
dc.subjectreturn timeen_US
dc.titleOn the relevance of q-distribution functions: The return time distribution of restricted random walkeren_US
dc.typeArticleen_US

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