Abstract. We prove universality at the edge of the spectrum for unitary (β = 2), orthogonal (β = 1) and symplectic (β = 4) ensembles of random matrices in the scaling limit for a class of weights w(x) = e (x) where V is a polynomial, V (x) = κ2mx + · · · , κ2m > 0. The precise statement of our results is given in Theorem 1.1 and Corollaries 1.2, 1.3 below. For a proof of universality in the bul...