Asymptotics of Selberg-like integrals by lattice path counting

Details Asymptotics of Selberg-like integrals by lattice path counting Asymptotics of Selberg-like integrals by lattice path counting

2011-11-22

arxiv.org/abs/1111.5181v1

Annals of Physics 326 (2011), 828-838

Physics

Mathematical Physics

Scientific paper

10.1016/j.aop.2010.09.007

We obtain explicit expressions for positive integer moments of the probability density of eigenvalues of the Jacobi and Laguerre random matrix ensembles, in the asymptotic regime of large dimension. These densities are closely related to the Selberg and Selberg-like multidimensional integrals. Our method of solution is combinatorial: it consists in the enumeration of certain classes of lattice paths associated to the solution of recurrence relations.

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