Generic regularity of equilibrium measures for the logarithmic potential with external fields

Abstract

It is a well-known conjecture in $\beta$-models and in their discrete counterpart that, generically, external potentials should be ``off-critical'' (or, equivalently, ``regular''). Exploiting the connection between minimizing measures and thin obstacle problems, we give a positive answer to this conjecture.

Published in Comm. Math. Phys