# Breaking Bivariate Records

## TL;DR

This paper investigates the properties of bivariate Pareto records for independent uniform observations, revealing that the distribution of records broken by a new record-setting observation is asymptotically geometric with parameter 1/2.

## Contribution

It establishes a fundamental property of bivariate Pareto records, specifically the asymptotic distribution of broken records conditioned on setting a record.

## Key findings

- Asymptotic conditional distribution is Geometric with parameter 1/2.
- Provides theoretical insight into bivariate Pareto record behavior.
- Enhances understanding of record-breaking processes in bivariate data.

## Abstract

We establish a fundamental property of bivariate Pareto records for independent observations uniformly distributed in the unit square. We prove that the asymptotic conditional distribution of the number of records broken by an observation given that the observation sets a record is Geometric with parameter 1/2.