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Large deviations and linear statistics for potential theoretic ensembles associated with regular closed sets
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  • Published: 18 July 2012

Large deviations and linear statistics for potential theoretic ensembles associated with regular closed sets

  • Maxim L. Yattselev1 

Probability Theory and Related Fields volume 156, pages 827–850 (2013)Cite this article

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Abstract

A two-dimensional statistical model of N charged particles interacting via logarithmic repulsion in the presence of an oppositely charged regular closed region K whose charge density is determined by its equilibrium potential at an inverse temperature β is investigated. When the charge on the region, s, is greater than N, the particles accumulate in a neighborhood of the boundary of K, and form a point process in the complex plane. We describe the weak* limits of the joint intensities of this point process and show that it is exponentially likely to find the process in a neighborhood of the equilibrium measure for K.

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Authors and Affiliations

  1. Department of Mathematics, University of Oregon, Eugene, OR, 97403, USA

    Maxim L. Yattselev

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  1. Maxim L. Yattselev
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Correspondence to Maxim L. Yattselev.

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Yattselev, M.L. Large deviations and linear statistics for potential theoretic ensembles associated with regular closed sets. Probab. Theory Relat. Fields 156, 827–850 (2013). https://doi.org/10.1007/s00440-012-0444-1

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  • Received: 19 March 2012

  • Published: 18 July 2012

  • Issue Date: August 2013

  • DOI: https://doi.org/10.1007/s00440-012-0444-1

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Keywords

  • Normal matrix model
  • Potential theoretic ensembles
  • Large deviation principle
  • Linear statistics

Mathematics Subject Classification (2000)

  • 60F10
  • 15B52
  • 15A18
  • 31A15
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