On the minimum of several random variables
Authors:
Y. Gordon, A. E. Litvak, C. Schütt and E. Werner
Journal:
Proc. Amer. Math. Soc. 134 (2006), 36653675
MSC (2000):
Primary 62G30, 60E15, 60G51
Published electronically:
May 31, 2006
MathSciNet review:
2240681
Fulltext PDF Free Access
Abstract 
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Abstract: For a given sequence of real numbers , we denote the th smallest one by . Let be a class of random variables satisfying certain distribution conditions (the class contains Gaussian random variables). We show that there exist two absolute positive constants and such that for every sequence of real numbers and every , one has  where are independent random variables from the class . Moreover, if , then the lefthand side estimate does not require independence of the 's. We provide similar estimates for the moments of as well.
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Additional Information
Y. Gordon
Affiliation:
Department of Mathematics, Technion, Haifa 32000, Israel
Email:
gordon@techunix.technion.ac.il
A. E. Litvak
Affiliation:
Department of Mathematics and Statistics Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email:
alexandr@math.ualberta.ca
C. Schütt
Affiliation:
Mathematisches Seminar, Christian Albrechts Universität, 24098 Kiel, Germany
Email:
schuett@math.unikiel.de
E. Werner
Affiliation:
Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106 and Université de Lille 1, UFR de Mathématique, 59655 Villeneuve d’Ascq, France
Email:
emw2@po.cwru.edu
DOI:
http://dx.doi.org/10.1090/S000299390608453X
PII:
S 00029939(06)08453X
Keywords:
Order statistics,
expectations,
moments,
normal distribution,
exponential distribution.
Received by editor(s):
March 7, 2005
Received by editor(s) in revised form:
June 25, 2005
Published electronically:
May 31, 2006
Additional Notes:
The first author was partially supported by the Fund for the Promotion of Research at the Technion and by FranceIsrael Cooperation agreement #31350
The first and third authors were partially supported by FP6 Marie Curie Actions, MRTNCT2004511953, PHD
The fourth author was partially supported by an NSF Grant, by a Nato Collaborative Linkage Grant, and by an NSF Advance Opportunity Grant
Communicated by:
N. TomczakJaegermann
Article copyright:
© Copyright 2006
American Mathematical Society
