Large n Limit of Gaussian Random Matrices with External Source, Part I

By Pavel Bleher, Arno B. J. Kuijlaars. 2004

182 citations recorded by the source corpus.

AbstractWe consider the random matrix ensemble with an external source defined on n×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→∞, 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 3×3-matrix Riemann-Hilbert problem, and the Deift/Zhou steepest descent method to analyze the Riemann-Hilbert problem in the large n limit.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f961603913d8c07acd0e5faee52e2267b6fec4a3

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In Applied Mathematics

  1. Arno B. J. Kuijlaars
  2. Andrei Martínez-Finkelshtein
  3. Alexander I. Aptekarev
  4. Pavel Bleher
  5. Walter Van Assche
  6. K. Mclaughlin
  7. Maxim L. Yattselev

In Mathematical Physics

  1. Arno B. J. Kuijlaars

In Statistics and Probability

  1. Arno B. J. Kuijlaars
  2. Pavel Bleher

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