The limit distribution of the largest interpoint distance for distributions supported by an ellipse and generalizations

TL;DR

This paper investigates the asymptotic distribution of the maximum distance between points randomly placed within an elliptical boundary, providing insights into the behavior for uniform distributions in such shapes.

Contribution

It characterizes the limit distribution of the largest interpoint distance for points in elliptical and similar bounded planar sets.

Findings

Derived the asymptotic distribution for uniform points in an ellipse

Extended results to more general boundary shapes with elliptical behavior

Provided theoretical foundations for understanding extreme interpoint distances

Abstract

We study the asymptotic behaviour of the maximum interpoint distance of random points in a planar bounded set with an unique major axis and a boundary behaving like an ellipse at the endpoints. Our main result covers the case of uniformly distributed points in an ellipse.