2 research outputs found
Moment determinants as isomonodromic tau functions
We consider a wide class of determinants whose entries are moments of the
so-called semiclassical functionals and we show that they are tau functions for
an appropriate isomonodromic family which depends on the parameters of the
symbols for the functionals. This shows that the vanishing of the tau-function
for those systems is the obstruction to the solvability of a Riemann-Hilbert
problem associated to certain classes of (multiple) orthogonal polynomials. The
determinants include Haenkel, Toeplitz and shifted-Toeplitz determinants as
well as determinants of bimoment functionals and the determinants arising in
the study of multiple orthogonality. Some of these determinants appear also as
partition functions of random matrix models, including an instance of a
two-matrix model.Comment: 24 page