## Annals of Probability

### Limiting Curves for I.I.D. Records

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 23, Number 2 (1995), 852-878.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176988293

Digital Object Identifier
doi:10.1214/aop/1176988293

Mathematical Reviews number (MathSciNet)
MR1334175

Zentralblatt MATH identifier
0834.60058

JSTOR