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

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

2006-05-04

arxiv.org/abs/math-ph/0605010v1

Physics

Mathematical Physics

latex, 1 figure, 55 pages

Scientific paper

10.1088/0305-4470/39/49/004

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.

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