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Free point processes and free extreme values
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  • Published: 05 March 2009

Free point processes and free extreme values

  • G. Ben Arous1 &
  • V. Kargin2 

Probability Theory and Related Fields volume 147, pages 161–183 (2010)Cite this article

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  • 5 Citations

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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.

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Author information

Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY, 10012, USA

    G. Ben Arous

  2. Department of Mathematics, Stanford University, Palo Alto, CA, 94305, USA

    V. Kargin

Authors
  1. G. Ben Arous
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  2. V. Kargin
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Corresponding author

Correspondence to G. Ben Arous.

Additional information

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

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Cite this article

Ben Arous, G., Kargin, V. Free point processes and free extreme values. Probab. Theory Relat. Fields 147, 161–183 (2010). https://doi.org/10.1007/s00440-009-0204-z

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  • Received: 04 August 2008

  • Revised: 15 January 2009

  • Published: 05 March 2009

  • Issue Date: May 2010

  • DOI: https://doi.org/10.1007/s00440-009-0204-z

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Mathematics Subject Classification (2000)

  • 46L54
  • 62G32
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