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Title: Scaling exponents for ordered maxima

Abstract

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.

Authors:
 [1];  [2];  [1]
+ Show Author Affiliations
  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)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1239571
Alternate Identifier(s):
OSTI ID: 1234086
Report Number(s):
LA-UR-15-28155
Journal ID: ISSN 1539-3755; PLEEE8
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Additional Journal Information:
Journal Volume: 92; Journal Issue: 6; Journal ID: ISSN 1539-3755
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; extreme-value statistics

Citation Formats

Ben-Naim, E., Krapivsky, P. L., and Lemons, N. W. Scaling exponents for ordered maxima. United States: N. p., 2015. Web. doi:10.1103/PhysRevE.92.062139.
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Ben-Naim, E., Krapivsky, P. L., & Lemons, N. W. Scaling exponents for ordered maxima. United States. https://doi.org/10.1103/PhysRevE.92.062139
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Ben-Naim, E., Krapivsky, P. L., and Lemons, N. W. Tue . "Scaling exponents for ordered maxima". United States. https://doi.org/10.1103/PhysRevE.92.062139. https://www.osti.gov/servlets/purl/1239571.
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@article{osti_1239571,
title = {Scaling exponents for ordered maxima},
author = {Ben-Naim, E. and Krapivsky, P. L. and Lemons, N. W.},
abstractNote = {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.},
doi = {10.1103/PhysRevE.92.062139},
journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics},
number = 6,
volume = 92,
place = {United States},
year = {2015},
month = {12}
}
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https://doi.org/10.1103/PhysRevE.92.062139
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