Nonlinear Random Matrix Statistics, symmetric functions and hyperdeterminants

Abstract

Nonlinear statistics (i.e. statistics of permanents) on the eigenvalues of invariant random matrix models are considered for the three Dyson's symmetry classes $\beta =1,2,4$. General formulas in terms of hyperdeterminants are found for $\beta =2$. For specific cases and all $\beta$s, more computationally efficient results are obtained, based on symmetric functions expansions. As an application, we consider the case of quantum transport in chaotic cavities extending results from [D.V. Savin, H.-J. Sommers and W. Wieczorek, {\it Phys. Rev. B} {\bf 77}, 125332 (2008)].

16 pages, 4 figures

References in corpus (10)

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• Systematic approach to statistics of conductance and shot-noise in chaotic cavities
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Cited by in corpus (7)

• Moments of Wishart-Laguerre and Jacobi ensembles of random matrices: application to the quantum transport problem in chaotic cavities
• Universal covariance formula for linear statistics on random matrices
• Asymptotics of Selberg-like integrals: The unitary case and Newton's interpolation formula
• Largest Schmidt eigenvalue of entangled random pure states and conductance distribution in chaotic cavities
• Asymptotics of Selberg-like integrals by lattice path counting
• Zeros of the i.i.d. Gaussian Laurent series on an annulus: weighted Szegő kernels and permanental-determinantal point processes
• How to compute Selberg-like integrals?