The partition function of the twomatrix model as an isomonodromic τ function
Abstract
We consider the ItzyksonZuberEynardMehta twomatrix model and prove that the partition function is an isomonodromic τ function in a sense that generalizes that of Jimbo et al. [ "Monodromy preserving deformation of linear ordinary differential equations with rational coefficients," Physica D 2, 306 (1981)]. In order to achieve the generalization we need to define a notion of τ function for isomonodromic systems where the adregularity of the leading coefficient is not a necessary requirement.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 January 2009
 DOI:
 10.1063/1.3054865
 arXiv:
 arXiv:0809.1598
 Bibcode:
 2009JMP....50a3529B
 Keywords:

 02.10.Yn;
 02.10.De;
 02.30.Cj;
 Matrix theory;
 Algebraic structures and number theory;
 Measure and integration;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 22 pages, 1 figure