Vector Equilibrium Problems arising from Random Matrix models
Some random matrix models are known to have a limiting eigenvalue distribution, when the size of the
matrix goes to innity, characterized by an equilibrium problem arising from potential theory. This is the
case for the so-called orthogonal polynomial ensembles, for which eigenvalue distributions are controlled by
kernels involving orthogonal polynomials. Recently, it has been understood that some more complicated
random matrix models (as perturbated models, or multi-matrix models) have their limiting eigenvalue
distributions characterized by vector equilibrium problems, that is equilibrium problems involving more
than one measure. We will discuss some examples, their relation to multiple orthogonal polynomials,
and the technical diculties in the manipulation of such vector equilibrium problems (as the existence of
minimizers or regularity properties).
** This is a joint work with: A. Kuijlaars.