, Volume 147, Issue 1-2, pp 161-183
Date: 05 Mar 2009

Free point processes and free extreme values

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Abstract

We continue here the study of free extreme values begun in Ben Arous and Voiculescu (Ann Probab 34:2037–2059, 2006). We study the convergence of the free point processes associated with free extreme values to a free Poisson random measure (Voiculescu in Lecture notes in mathematics. Springer, Heidelberg, pp. 279–349, 1998; Barndorff-Nielsen and Thorbjornsen in Probab Theory Relat Fields 131:197–228, 2005). We relate this convergence to the free extremal laws introduced in Ben Arous and Voiculescu (Ann Probab 34:2037–2059, 2006) and give the limit laws for free order statistics.

Research supported in part by NSF Grants DMS 0808180, and OISE 0730136.