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Title: Large deviations for a non-centered Wishart matrix
Authors: Hardy, Adrien ×
Kuijlaars, Arno #
Issue Date: 2013
Publisher: World Scientific Publishing Co. Pte. Ltd.
Series Title: Random Matrices: Theory and Application vol:2 issue:1
Article number: 1250016
Abstract: We investigate an additive perturbation of a complex Wishart random matrix and prove that a large deviation principle holds for the spectral measures. The rate function is associated to a vector equilibrium problem coming from logarithmic potential theory, which in our case is a quadratic map involving the logarithmic energies, or Voiculescu's entropies, of two measures in the presence of an external field and an upper constraint. The proof is based on a two type particles Coulomb gas representation for the eigenvalue distribution, which gives a new insight on why such variational problems should describe the limiting spectral distribution. This representation is available because of a Nikishin structure satisfied by the weights of the multiple orthogonal polynomials hidden in the background.
ISSN: 2010-3263
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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