Correlations between record events in sequences of random variables with a linear trend

TL;DR

This paper investigates the correlation structure of record events in sequences of independent random variables with a linearly changing mean, revealing complex patterns influenced by extreme value statistics.

Contribution

It provides a systematic analysis of record event correlations in non-i.i.d. sequences with linear trends, extending classical record theory.

Findings

Identifies positive and negative correlations between record events.

Shows asymptotic behavior governed by extreme value universality classes.

Extends understanding of record statistics beyond i.i.d. cases.

Abstract

The statistics of records in sequences of independent, identically distributed random variables is a classic subject of study. One of the earliest results concerns the stochastic independence of record events. Recently, records statistics beyond the case of i.i.d. random variables have received much attention, but the question of independence of record events has not been addressed systematically. In this paper, we study this question in detail for the case of independent, non-identically distributed random variables, specifically, for random variables with a linearly moving mean. We find a rich pattern of positive and negative correlations, and show how their asymptotics is determined by the universality classes of extreme value statistics.