Open Access
April, 1995 Limiting Curves for I.I.D. Records
Jean-Dominique Deuschel, Ofer Zeitouni
Ann. Probab. 23(2): 852-878 (April, 1995). DOI: 10.1214/aop/1176988293


We consider the concentration of measure for $n$ i.i.d., two-dimensional random variables under the conditioning that they form a record. Under mild conditions, we show that all random variables tend to concentrate, as $n \rightarrow \infty$, around limiting curves, which are the solutions of an appropriate variational problem. We also show that the same phenomenon occurs, without the records conditioning, for the longest increasing subsequence in the sample.


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Jean-Dominique Deuschel. Ofer Zeitouni. "Limiting Curves for I.I.D. Records." Ann. Probab. 23 (2) 852 - 878, April, 1995.


Published: April, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0834.60058
MathSciNet: MR1334175
Digital Object Identifier: 10.1214/aop/1176988293

Primary: 60G70
Secondary: 60F10

Keywords: large deviations , Longest increasing subsequence , records

Rights: Copyright © 1995 Institute of Mathematical Statistics

Vol.23 • No. 2 • April, 1995
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