Free point processes and free extreme values

G. Ben Arous, V. Kargin

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)161-183
Number of pages23
JournalProbability Theory and Related Fields
Volume147
Issue number1
DOIs
StatePublished - Feb 2010

Fingerprint

Extreme Values
Point Process
Poisson Random Measure
Limit Laws
Order Statistics
Field Theory
Continue
Extreme values
Point process
Field theory
Mathematics
Order statistics

ASJC Scopus subject areas

  • Statistics and Probability
  • Analysis
  • Statistics, Probability and Uncertainty

Cite this

Free point processes and free extreme values. / Arous, G. Ben; Kargin, V.

In: Probability Theory and Related Fields, Vol. 147, No. 1, 02.2010, p. 161-183.

Research output: Contribution to journalArticle

@article{65525cd65c7544fe87b3a8903246e202,
title = "Free point processes and free extreme values",
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.",
author = "Arous, {G. Ben} and V. Kargin",
year = "2010",
month = "2",
doi = "10.1007/s00440-009-0204-z",
language = "English (US)",
volume = "147",
pages = "161--183",
journal = "Probability Theory and Related Fields",
issn = "0178-8051",
publisher = "Springer New York",
number = "1",

}

TY - JOUR

T1 - Free point processes and free extreme values

AU - Arous, G. Ben

AU - Kargin, V.

PY - 2010/2

Y1 - 2010/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=76949093540&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=76949093540&partnerID=8YFLogxK

U2 - 10.1007/s00440-009-0204-z

DO - 10.1007/s00440-009-0204-z

M3 - Article

AN - SCOPUS:76949093540

VL - 147

SP - 161

EP - 183

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 1

ER -