Mixed correlation function and spectral curve for the 2-matrix model

Abstract

We compute the mixed correlation function in a way which involves only the orthogonal polynomials with degrees close to $n$, (in some sense like the Christoffel Darboux theorem for non-mixed correlation functions). We also derive new representations for the differential systems satisfied by the biorthogonal polynomials, and we find new formulae for the spectral curve. In particular we prove the conjecture of M. Bertola, claiming that the spectral curve is the same curve which appears in the loop equations.

latex, 1 figure, 55 pages

References in corpus (4)

• Biorthogonal Polynomials for Potentials of two Variables and External Sources at the Denominator
• A short note about Morozov's formula
• The 2-matrix model, biorthogonal polynomials, Riemann-Hilbert problem, and algebraic geometry
• Orthogonal Polynomials for Potentials of two Variables with External Sources

Cited by in corpus (4)

• Topological expansion of mixed correlations in the hermitian 2 Matrix Model and x-y symmetry of the F_g invariants
• The partition function of the two-matrix model as an isomonodromic tau-function
• Generalized Christoffel-Darboux formula for classical skew-orthogonal polynomials
• Universality in the two matrix model: a Riemann-Hilbert steepest descent analysis