Fluctuations of eigenvalues of matrix models and their applications

Details Fluctuations of eigenvalues of matrix models and their applications Fluctuations of eigenvalues of matrix models and their applications

2010-03-31

arxiv.org/abs/1003.6121v1

Physics

Mathematical Physics

22 pages

Scientific paper

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 $V$.

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