Universality in the Two Matrix Model: a Riemann-hilbert Steepest Descent Analysis

@inproceedings{Kuijlaars2008UniversalityIT,
  title={Universality in the Two Matrix Model: a Riemann-hilbert Steepest Descent Analysis},
  author={Arno B. J. Kuijlaars},
  year={2008}
}
The eigenvalue statistics of a pair (M1, M2) of n × n Her-mitian matrices taken random with respect to the measure 1 Zn exp`− n Tr(V (M1) + W (M2) − τ M1M2) ´ dM1dM2 can be described in terms of two families of biorthogonal polynomials. In this paper we give a steepest descent analysis of a 4 × 4 matrix-valued Riemann-Hilbert problem characterizing one of the families of biorthog-onal polynomials in the special case W (y) = y 4 /4 and V an even polynomial. As a result we obtain the limiting… CONTINUE READING
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