Satya N. Majumdar, Robert M. Ziff
Published 2008-05-31, updated 2008-08-04Version 2
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.
Comments: 4 pages, 3 figures. Added journal ref. and made small changes. Compatible with published version
Journal: Physical Review Letters 101, 050601 (1 August 2008)
Exact Statistics of the Gap and Time Interval Between the First Two Maxima of Random Walks
Mean first-passage time for random walks in general graphs with a deep trap
Universal record statistics for random walks and Lévy flights with a nonzero staying probability
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