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Random normal matrices and Ward identities

  • Ameur, Yacin [1] ; Hedenmalm, Haakan [2] ; Makarov, Nikolai [3]
    1. [1] Lund University

      Lund University

      Suecia

    2. [2] Royal Institute of Technology

      Royal Institute of Technology

      Suecia

    3. [3] California Institute of Technology

      California Institute of Technology

      Estados Unidos

  • Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 43, Nº. 3, 2015, págs. 1157-1201
  • Idioma: inglés
  • DOI: 10.1214/13-AOP885
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  • Resumen
    • We consider the random normal matrix ensemble associated with a potential in the plane of sufficient growth near infinity. It is known that asymptotically as the order of the random matrix increases indefinitely, the eigenvalues approach a certain equilibrium density, given in terms of Frostman’s solution to the minimum energy problem of weighted logarithmic potential theory. At a finer scale, we may consider fluctuations of eigenvalues about the equilibrium. In the present paper, we give the correction to the expectation of the fluctuations, and we show that the potential field of the corrected fluctuations converge on smooth test functions to a Gaussian free field with free boundary conditions on the droplet associated with the potential.


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