Universality in invariant random-matrix models: Existence near the soft edge
- 1 March 1997
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 55 (3) , 3712-3715
- https://doi.org/10.1103/physreve.55.3712
Abstract
We consider two non-Gaussian ensembles of large Hermitian random matrices with strong level confinement and show that near the soft edge of the spectrum both scaled density of states and eigenvalue correlations follow so-called Airy laws inherent in the Gaussian unitary ensemble. This suggests that the invariant one-matrix models should display universal eigenvalue correlations in the soft-edge scaling limit.Keywords
All Related Versions
This publication has 14 references indexed in Scilit:
- Theory of random matrices with strong level confinement: Orthogonal polynomial approachPhysical Review E, 1996
- Unitary random-matrix ensemble with governable level confinementPhysical Review E, 1996
- Universality of Random-Matrix Results for Non-Gaussian EnsemblesPhysical Review Letters, 1995
- Level-spacing distributions and the Airy kernelCommunications in Mathematical Physics, 1994
- Nonperturbative two-dimensional quantum gravityPhysical Review Letters, 1990
- A proof of Freud's conjecture for exponential weightsConstructive Approximation, 1988
- Asymptotics for solutions of smooth recurrence equationsProceedings of the American Mathematical Society, 1985
- Asymptotics for Orthogonal Polynomials Associated with $\exp ( - x^4 )$SIAM Journal on Mathematical Analysis, 1984
- Nonnegative solutions of a nonlinear recurrenceJournal of Approximation Theory, 1983
- A differential equation for orthogonal polynomialsDuke Mathematical Journal, 1939