The Spectrum of the Fractional Laplacian and First Passage Time Statistics

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dc.creatorKatzav, E.
dc.creatorAdda-Bedia, M.
dc.date2008-02-08
dc.date2008-05-28
dc.date.accessioned2026-07-07T09:50:48Z
dc.date.available2026-07-07T09:50:48Z
dc.descriptionWe present exact results for the spectrum of the fractional Laplacian in a bounded domain and apply them to First Passage Time (FPT) Statistics of Lévy flights. We specifically show that the average is insufficient to describe the distribution of FPT, although it is the only quantity available in the existing literature. In particular, we show that the FPT distribution is not peaked around the average, and that knowledge of the whole distribution is necessary to describe this phenomenon. For this purpose, we provide an efficient method to calculate higher order cumulants and the whole distribution.
dc.description10 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/0802.1166
dc.identifierhttp://arxiv.org/abs/0802.1166
dc.identifierEurophys. Lett 83 30006 (2008)
dc.identifierdoi:10.1209/0295-5075/83/30006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/165072
dc.subjectStatistical Mechanics
dc.subjectDisordered Systems and Neural Networks
dc.subjectSoft Condensed Matter
dc.titleThe Spectrum of the Fractional Laplacian and First Passage Time Statistics
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