Limiting curves for i.i.d. records
type: Item
instance of: scholarly article
title: Limiting curves for i.i.d. records
zbMATH Open document ID: 0834.60058
published in: The Annals of Probability
publication date: 1996-03-25T00:00:00Z
review text: For independent bivariate vectors \((X_i, Y_i)\), \(i \geq 1\), define \(L_n\) as \(L_n = \infty\) if \(L_{n - 1} = \infty\) and \(L_n = \inf \{m > L_{n - 1} : X_m > \max (X_j : 1 \leq j \leq m - 1)\) and \(Y_m > \max (Y_j : 1 \leq j \leq m - 1)\}\) if \(L_{n - 1} < \infty\). Set \(R_n = (X_{L_n}, Y_{L_n})\) if \(L_n < \infty\). The authors show that, under some assumptions, the records \(R_n\) concentrate around limiting curves which form the solution of a variational problem. This variational problem is studied in detail. The relation of the preceding problem to the longest increasing subsequence problem is pointed out.
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 796524
zbMATH Keywords: simultaneous record times
zbMATH Keywords: records
zbMATH Keywords: limiting curves
zbMATH Keywords: variational problem
zbMATH Keywords: longest increasing subsequence problem
author: Jean-Dominique Deuschel
author: Ofer Zeitouni
reviewed by: Janos Galambos
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176988293
OpenAlex ID: W2002114058
DOI: 10.1214/AOP/1176988293
description: scientific article; zbMATH DE number 796524