Fluctuations of eigenvalues of matrix models and their applications

Abstract

We study the expectation of linear eigenvalue statistics of matrix models with any $\beta >0$, assuming that the potential $V$ is a real analytic function and that the corresponding equilibrium measure has a one-interval support. We obtain the first order (with respect to $n^{-1}$) correction terms for the expectation and apply this result to prove bulk universality for real symmetric and symplectic matrix models with the same $V$.

22 pages

References in corpus (2)

• Universality at the edge of the spectrum for unitary, orthogonal and symplectic ensembles of random matrices
• The dbar steepest descent method for orthogonal polynomials on the real line with varying weights

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