Second order asymptotics for matrix models. (English) Zbl 1129.15020

The asymptotical behaviour of Hermitian random matrices whose distribution is given by a small convex perturbation of the Gaussian unitary ensemble is studied. \(m\)-tuples of random matrices are considered. The first order correction to the free energy is expressed as a generating function for the enumeration of maps. This is done by proving a central limit theorem for some specific polynomials and also for arbitrary polynomials. An interpretation of the variance and of the free energy in terms of a generating function for the number of planar maps is given. Finally, the second order correction to the free energy is computed.


15B52 Random matrices (algebraic aspects)
05C30 Enumeration in graph theory
60F05 Central limit and other weak theorems
Full Text: DOI arXiv Euclid


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