Asymptotics of Selberg-like integrals by lattice path counting

Abstract

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.

References in corpus (4)

• Systematic approach to statistics of conductance and shot-noise in chaotic cavities
• Nonlinear statistics of quantum transport in chaotic cavities
• Statistics of quantum transport in chaotic cavities with broken time-reversal symmetry
• Full counting statistics of chaotic cavities with many open channels

Cited by in corpus (7)

• Moments of the transmission eigenvalues, proper delay times and random matrix theory II
• Correlators for the Wigner-Smith time-delay matrix of chaotic cavities
• Statistical distribution of the Wigner-Smith time-delay matrix moments for chaotic cavities
• Large-$N$ expansion for the time-delay matrix of ballistic chaotic cavities
• Integer moments of complex Wishart matrices and Hurwitz numbers
• Universal covariance formula for linear statistics on random matrices
• Large deviation eigenvalue density for the soft edge Laguerre and Jacobi $\beta$-ensembles