2008/06/30 by Satya N. Majumdar, Robert M. Ziff
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Bayesian Methods and Mixture Models #Diffusion and Search Dynamics #Stochastic processes and statistical mechanics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.101.050601
published as Physical Review Letters 101, 050601 (1 August 2008) · 4 pages, 3 figures. Added journal ref. and made small changes. Compatible with published version
openalex publication_date 2008/08/01 · arxiv created 2008/08/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 0.626 508...N, respectively. The case of a discrete random walker is also studied, and similar asymptotic behavior is found.