Universal Record Statistics of Random Walks and Lévy Flights

Details Universal Record Statistics of Random Walks and Lévy Flights Universal Record Statistics of Random Walks and Lévy Flights

2008-05-31

arxiv.org/abs/0806.0057v2

Physical Review Letters 101, 050601 (1 August 2008)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures. Added journal ref. and made small changes. Compatible with published version

Scientific paper

10.1103/PhysRevLett.101.050601

It is shown that statistics of records for time series generated by random walks are independent of the details of the jump distribution, as long as the latter is continuous and symmetric. In N steps, the mean of the record distribution grows as the sqrt(4N/pi) while the standard deviation grows as sqrt((2-4/pi) N), so the distribution is non-self-averaging. The mean shortest and longest duration records grow as sqrt(N/pi) and 0.626508... N, respectively. The case of a discrete random walker is also studied, and similar asymptotic behavior is found.

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