Highly Influenced

# 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} }

- Published 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

Highly Cited

This paper has 18 citations. REVIEW CITATIONS

#### From This Paper

##### Figures, tables, and topics from this paper.

11 Citations

72 References

Similar Papers