Theory of random matrices with strong level confinement: Orthogonal polynomial approach.
@article{Freilikher1996TheoryOR, title={Theory of random matrices with strong level confinement: Orthogonal polynomial approach.}, author={Freilikher and Kanzieper and Yurkevich}, journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics}, year={1996}, volume={54 1}, pages={ 210-219 } }
Unitary ensembles of large N x N random matrices with a non-Gaussian probability distribution P[H] ~ exp{-TrV[H]} are studied using a theory of polynomials orthogonal with respect to exponential weights. Asymptotically exact expressions for density of levels, one- and two-point Green's functions are calculated. We show that in the large-N limit the properly rescaled local eigenvalue correlations are independent of P[H] while global smoothed connected correlations depend on P[H] only through the…
9 Citations
Random-matrix models with the logarithmic-singular level confinement : method of fictitious fermions
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Abstract A joint distribution function of N eigenvalues of a U(N) invariant random-matrix ensemble can be interpreted as a probability density of finding N fictitious non-interacting fermions to be…
Spectra of large random matrices: A method of study
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A formalism for study of spectral correlations in non-Gaussian, unitary invariant ensembles of large random matrices with strong level confinement is reviewed. It is based on the Shohat method in the…
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The correlation function is an important quantity in the physics of ultracold quantum gases because it provides information about the quantum many-body wave function beyond the simple density…
Statistical distribution of the Wigner-Smith time-delay matrix moments for chaotic cavities.
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The joint distribution of the moments TrQ(κ) (κ≥1) of the Wigner-Smith matrix for a chaotic cavity supporting a large number of scattering channels n turns out to be asymptotically Gaussian.
Optimality of Kernel Density Estimation of Prior Distribution in Bayes Network
- Mathematics, Computer ScienceICONIP
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This paper adopts general naive Bayes to handle continuous variables, and proposes a kind of kernel function constructed by orthogonal polynomials, which is used to estimate the density function of prior distribution in Bayes network.
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