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On tau functions for orthogonal polynomials and matrix models

2011
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Journal of Physics A: Mathematical and Theoretical
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Let v be a real polynomial of even degree, and let \rho be the equilibrium probability measure for v with support S; so that v(x)\geq 2\int \log |x-y| \rho (dy)+C_v for some constant C_v with support S. Then S is the union of finitely many bounded intervals with endpoints delta_j, and \rho is given by an algebrais weight w(x) on S. The system of orthogonal polynomials for w gives rise to the Magnus--Schlesinger differential equations. This paper identifies the tau function of this system with

doi:10.1088/1751-8113/44/28/285202
fatcat:dzpstcxf3vgznfrpqbsses3fpq