Universality limits for exponential weights

We establish universality in the bulk for fixed exponential weights on the whole real line. Our methods involve first-order asymptotics for orthogonal polynomials and localization techniques. In particular, we allow exponential weights such as | x | ^2β g ²(x)exp∈(-2Q(x)), where β>-1/2, Q is convex and Q ^″ satisfies some regularity conditions, while g is positive, and has a uniformly continuous and slowly growing or decaying logarithm.