### Discrete Painlevé equations and orthogonal polynomials.

Its, A *(Indiana University Indianapolis)*

Friday 03 July 2009, 09:00-10:00

Seminar Room 1, Newton Institute

#### Abstract

Random matrices and orthogonal polynomials have been, for more than a decade, one of the principal sources of the important analytical ideas and exciting problems in the theory of discrete Painleve equations. In the orthogonal polynomial setting, the discrete Painleve equations appear in the form of the nonlinear difference relations satisfied by the relevant recurrence coefficients. The principal analytical question is the analysis of certain double-scaling limits of the solutions of the discrete Painleve equations. In the talk we will present a review on the subject using the Riemann-Hilbert formalism as a main analytic tool. The Riemann-Hilbert approach in the theory of discrete Painleve equations will be outlined as well.

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