# 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

- Physics
- 1997

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

- Mathematics
- 1999

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…

A unified fluctuation formula for one-cut β -ensembles of random matrices

- Mathematics, Computer Science
- 2015

Using a Coulomb gas approach, the generating function of the covariances of power traces for one-cut β-ensembles of random matrices in the limit of large matrix size is computed and is universal for a large class of models.

Factorization of Correlation Functions and the Replica Limit of the Toda Lattice Equation

- Physics, Mathematics
- 2004

Higher-order local and non-local correlations for 1D strongly interacting Bose gas

- Physics
- 2016

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.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

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
- 2006

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.

## References

SHOWING 1-3 OF 3 REFERENCES

Introduction to the Supersymmetry Method for the Gaussian Random-Matrix Ensembles

- Physics
- 1994

This article is intended to provide a pedagogical introduction to the supersymmetry method for performing ensemble-averaging in Gaussian random-matrix theory. The method is illustrated by a detailed…

Theory of linear operators in Hilbert space

- Mathematics
- 1961

linear operators in hilbert spaces | springerlink abstract. we recall some fundamental notions of the theory of linear operators in hilbert spaces which are required for a rigorous formulation of the…