Monodromy approach to the scaling limits in the isomonodromy systems

Abstract

The isomonodromy deformation method is applied to the scaling limits in the linear NxN matrix equations with rational coefficients to obtain the deformation equations for the algebraic curves which describe the local behavior of the reduced versions for the relevant isomonodromy deformation equations. The approach is illustrated by the study of the algebraic curve associated to the n-large asymptotics in the sequence of the bi-orthogonal polynomials with cubic potentials.

Latex, 15 pages, 1 figure; submitted to the proceedings of the conference NEEDS 2002; in compare to the original version, there are minor changes in the references and in the main body of the article

References in corpus (3)

• Duality, Biorthogonal Polynomials and Multi-Matrix Models
• The Riemann-Hilbert Problem for the Bi-Orthogonal Polynomials
• HCIZ integral and 2D Toda lattice hierarchy

Cited by in corpus (5)

• Quasi-linear Stokes phenomenon for the Painlevé first equation
• Large-degree asymptotics of rational Painleve-II functions. II
• Poles of Integrale Tritronquee and Anharmonic Oscillators. Asymptotic localization from WKB analysis
• Numerical Approach to Painlevé Transcendents on Unbounded Domains
• On the tritronquée solutions of P${}_I^2$