Title: Large n limit of Gaussian random matrices with external source, part I
Authors: Bleher, P ×
Kuijlaars, Arno #
Issue Date: 2004
Publisher: SPRINGER
Series Title: Communications in mathematical physics vol:252 issue:1-3 pages:43-76
Abstract: We consider the random matrix ensemble with an external source 1/Z_n e(-n Tr)((1/2)M_2)- AM) dM defined on n x n Hermitian matrices, where A is a diagonal matrix with only two eigenvalues +/-a of equal multiplicity. For the case a > 1, we establish the universal behavior of local eigenvalue correlations in the limit n --> infinity, which is known from unitarily invariant random matrix models. Thus, local eigenvalue correlations are expressed in terms of the sine kernel in the bulk and in terms of the Airy kernel at the edge of the spectrum. We use a characterization of the associated multiple Hermite polynomials by a 3 x 3-matrix Riemann-Hilbert problem, and the Deift/Zhou steepest descent method to analyze the Riemann-Hilbert problem in the large n limit.
ISSN: 0010-3616
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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