Universal Record Statistics of Random Walks and L\'evy Flights
Statistical Mechanics
2008-08-04 v2
Abstract
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.
Keywords
Cite
@article{arxiv.0806.0057,
title = {Universal Record Statistics of Random Walks and L\'evy Flights},
author = {Satya N. Majumdar and Robert M. Ziff},
journal= {arXiv preprint arXiv:0806.0057},
year = {2008}
}
Comments
4 pages, 3 figures. Added journal ref. and made small changes. Compatible with published version