TY - JOUR
T1 - The spectrum of the fractional Laplacian and first-passage-time statistics
AU - Katzav, E.
AU - Adda-Bedia, M.
PY - 2008/8/1
Y1 - 2008/8/1
N2 - 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 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.
AB - 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 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.
UR - http://www.scopus.com/inward/record.url?scp=79051471420&partnerID=8YFLogxK
U2 - 10.1209/0295-5075/83/30006
DO - 10.1209/0295-5075/83/30006
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AN - SCOPUS:79051471420
SN - 0295-5075
VL - 83
JO - Lettere Al Nuovo Cimento
JF - Lettere Al Nuovo Cimento
IS - 3
M1 - 30006
ER -