Number of distinct sites visited by a subdiffusive random walker

The asymptotic mean number of distinct sites visited by a subdiffusive continuous-time random walker in two dimensions seems not to have been explicitly calculated anywhere in the literature. This number has been calculated for other dimensions for only one specific asymptotic behavior of the waitin...

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Published inPhysical review. E, Statistical, nonlinear, and soft matter physics Vol. 77; no. 3 Pt 1; p. 032101
Main Authors Yuste, Santos Bravo, Klafter, J, Lindenberg, Katja
Format Journal Article
LanguageEnglish
Published United States 01.03.2008
Subjects
Algorithms
Biological Transport
Biophysics - methods
Diffusion
Kinetics
Models, Statistical
Models, Theoretical
Movement
Probability
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Summary:The asymptotic mean number of distinct sites visited by a subdiffusive continuous-time random walker in two dimensions seems not to have been explicitly calculated anywhere in the literature. This number has been calculated for other dimensions for only one specific asymptotic behavior of the waiting time distribution between steps. We present an explicit derivation for two cases in all integer dimensions so as to formally complete a tableau of results. In this tableau we include the dominant as well as subdominant contributions in all integer dimensions. Other quantities that can be calculated from the mean number of distinct sites visited are also discussed.
ISSN:1539-3755
DOI:10.1103/PhysRevE.77.032101