Free point processes and free extreme values
G. Ben Arous, V. Kargin
TL;DR
This paper advances the understanding of free extreme values by analyzing the convergence of free point processes to free Poisson measures and establishing limit laws for free order statistics.
Contribution
It extends previous work by establishing convergence results and limit laws for free extreme values and order statistics in free probability theory.
Findings
Convergence of free point processes to free Poisson measures.
Limit laws for free extremal values.
Characterization of free order statistics.
Abstract
We continue here the study of free extreme values begun in Ben Arous and Voiculescu (2006). We study the convergence of the free point processes associated with free extreme values to a free Poisson random measure (Voiculescu (1998), Barndorff-Nielsen and Thorbjornsen (2005)). We relate this convergence to the free extremal laws introduced in Ben Arous and Voiculescu (2006) and give the limit laws for free order statistics.
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Taxonomy
TopicsRandom Matrices and Applications · Stochastic processes and statistical mechanics · Stochastic processes and financial applications