Statistics Papers

Document Type

Journal Article

Date of this Version

1-1979

Publication Source

Journal für die Reine und Angewandte Mathematik

Volume

1979

Issue

306

Start Page

49

Last Page

59

DOI

10.1515/crll.1979.306.49

Abstract

Hammersley [7] showed that if X1, X2, . . . is a sequence of independent identically distributed random variables whose common distribution is continuous, and if ln+(ln-) denotes the length of the longest increasing (decreasing) subsequence of X1, X2, . . ., Xn, then there is a constant c such that ln-⁄n½c and ln+⁄n½c in probability, as n → ∞. Kesten [8] showed that in fact there is almost sure convergence. Logan and Shepp [11] proved that c ≧ 2, and recently Versik and Kerov [13] have announced that c = 2.

Copyright/Permission Statement

The original and published work is available at: https://www.degruyter.com/view/j/crll.1979.issue-306/crll.1979.306.49/crll.1979.306.49.xml

Comments

At the time of publication, author J. Michael Steele was affiliated with University of British Columbia. Currently, (s)he is a faculty member at the Statistic Department at the University of Pennsylvania.

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Date Posted: 27 November 2017

This document has been peer reviewed.