Minima and maxima of elliptical arrays and spherical processes

TL;DR

This paper studies the asymptotic behavior of minima and maxima in elliptical arrays and spherical processes, extending previous work and providing new insights into their extreme value distributions.

Contribution

It advances understanding of the asymptotics of elliptical array extrema and applies these results to spherical processes, building on prior research by Kabluchko.

Findings

Asymptotic behavior of minima of elliptical arrays analyzed.

Maxima of elliptical arrays in Gumbel or Weibull domains characterized.

Application to maxima and minima of independent spherical processes.

Abstract

In this paper, we investigate first the asymptotics of the minima of elliptical triangular arrays. Motivated by the findings of Kabluchko (Extremes 14 (2011) 285-310), we discuss further the asymptotic behaviour of the maxima of elliptical triangular arrays with marginal distribution functions in the Gumbel or Weibull max-domain of attraction. We present an application concerning the asymptotics of the maximum and the minimum of independent spherical processes.