The Fredholm determinant in (2) is well-defined since K [member of] [J.sub.1,loc](E, [mu]).
Takahashi, Random point fields associated with certain Fredholm determinants. I.
In this paper, we give solutions by means of Fredholm determinants of order 2N depending on 2N - 1 parameters and then by means of Wronskians of order 2N with 2N - 1 parameters.
So we get the solutions to (14) by means of Fredholm determinants.
With (24), the following link between Fredholm determinants and Wronskians is obtained:
The 13 papers consider such topics as nonlinear partial differential equations for Fredholm determinants
arising from string equations, a class of higher order Painlove systems arising from integrable hierarchies of type A, differential equations for triangle groups, the spectral curve of the Eynard-Orantin recursion via the Laplace transform, and continuum limits of Toda lattices for map enumeration.