Abstract
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|2βg2(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.
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