Duality of spectral curves arising in two-matrix models
Exactly Solvable and Integrable Systems
2007-05-23 v2 Statistical Mechanics
High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
The two matrix model is considered, with measure given by the exponential of a sum of polynomials in two different variables. It is shown how to derive a sequence of pairs of ``dual'' finite size systems of ODEs for the corresponding biorthonormal polynomials. An inverse theorem is proved showing how to reconstruct such measures from pairs of semi-infinite finite band matrices defining the recursion relations and satisfying the string equation. A proof is given in the limit that the dual systems obtained share the same spectral curve.
Keywords
Cite
@article{arxiv.nlin/0112006,
title = {Duality of spectral curves arising in two-matrix models},
author = {M. Bertola and B. Eynard and J. Harnad},
journal= {arXiv preprint arXiv:nlin/0112006},
year = {2007}
}
Comments
Write-up based on lecture by J. Harnad given at NEEDS 2001 Euroconference Isaac Newton Institute for Mathematical Sciences, Cambridge, U.K. July 24-31, 2001