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.
Citation
Jean-Dominique Deuschel. Ofer Zeitouni. "Limiting Curves for I.I.D. Records." Ann. Probab. 23 (2) 852 - 878, April, 1995. https://doi.org/10.1214/aop/1176988293
Information