标题： 两个矩阵模型中出现的谱曲线的对偶性 显示英文标题

标题： Duality of spectral curves arising in two-matrix models

摘要： 考虑了两个矩阵模型，其测度由两个不同变量的多项式和的指数给出。 展示了如何推导出对应双正交多项式的有限大小系统的“对偶”对序列。 证明了一个逆定理，说明如何从定义递推关系并满足字符串方程的无限阶有限带矩阵对中重建这些测度。 给出了在$N\to \infty$极限下的证明，表明所得的对偶系统共享相同的谱曲线。 显示英文摘要

摘要： 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 $N\to \infty$ limit that the dual systems obtained share the same spectral curve.