| Issue |
EPL
Volume 83, Number 3, August 2008
|
|
|---|---|---|
| Article Number | 30006 | |
| Number of page(s) | 6 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/83/30006 | |
| Published online | 17 July 2008 | |
The spectrum of the fractional Laplacian and First-Passage
Time statistics
Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, CNRS UMR 8550 24 rue Lhomond, 75231 Paris Cedex 05, France, EU
Corresponding author: eytan.katzav@lps.ens.fr
Received:
18
April
2008
Accepted:
9
June
2008
We present exact results for the spectrum of the fractional Laplacian in a bounded domain and apply them to First-PassageTime (FPT) statistics of Lévy flights. We specifically
show that the average is insufficient to describe the distribution of the 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.
PACS: 05.40.Fb – Random walks and Lévy flights / 02.50.-r – Probability theory, stochastic processes, and statistics / 89.65.Gh – Economics; econophysics, financial markets, business and management
© EPLA, 2008
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