The Spectrum of the Fractional Laplacian and First Passage Time Statistics

Details The Spectrum of the Fractional Laplacian and First Passage Time Statistics The Spectrum of the Fractional Laplacian and First Passage Time Statistics

2008-02-08

arxiv.org/abs/0802.1166v3

Europhys. Lett 83 30006 (2008)

Physics

Condensed Matter

Statistical Mechanics

10 pages, 6 figures

Scientific paper

10.1209/0295-5075/83/30006

We present exact results for the spectrum of the fractional Laplacian in a bounded domain and apply them to First Passage Time (FPT) Statistics of L\'evy 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.

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