4 papers
Duality of spectral curves arising in two-matrix models
M. Bertola, B. Eynard, J. Harnad
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 ``dua…
On the bilinear equations for Fredholm determinants appearing in random matrices
J. Harnad
It is shown how the bilinear differential equations satisfied by Fredholm determinants of integral operators appearing as spectral distribution functions for random matrices may be…
Picard-Fuchs Equations, Hauptmoduls and Integrable Systems
J. Harnad
The Schwarzian equations satisfied by certain Hauptmoduls (i.e., uniformizing functions for Riemann surfaces of genus zero) are derived from the Picard-Fuchs equations for families…
Modular Invariants and Generalized Halphen Systems
J. Harnad, J. McKay
Generalized Halphen systems are solved in terms of functions that uniformize genus zero Riemann surfaces, with automorphism groups that are commensurable with the modular group. Ra…