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Title: Scaling exponents for ordered maxima

Journal Article · · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
 [1];  [2];  [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Boston Univ., Boston, MA (United States); Univ. Paris-Saclay, Gif-sur-Yvette (France)
+ Show Author Affiliations

We study extreme value statistics of multiple sequences of random variables. For each sequence with N variables, independently drawn from the same distribution, the running maximum is defined as the largest variable to date. We compare the running maxima of m independent sequences and investigate the probability SN that the maxima are perfectly ordered, that is, the running maximum of the first sequence is always larger than that of the second sequence, which is always larger than the running maximum of the third sequence, and so on. The probability SN is universal: it does not depend on the distribution from which the random variables are drawn. For two sequences, SN~N–1/2, and in general, the decay is algebraic, SN~N–σm, for large N. We analytically obtain the exponent σ3≅1.302931 as root of a transcendental equation. Moreover, the exponents σm grow with m, and we show that σm~m for large m.

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC52-06NA25396
OSTI ID:
1239571
Alternate ID(s):
OSTI ID: 1234086
Report Number(s):
LA-UR-15-28155; PLEEE8
Journal Information:
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, Vol. 92, Issue 6; ISSN 1539-3755
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

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Record statistics of a strongly correlated time series: random walks and Lévy flights journal July 2017

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Related Subjects

97 MATHEMATICS AND COMPUTING
extreme-value statistics