Universality in invariant random-matrix models: Existence near the soft edge

Details Universality in invariant random-matrix models: Existence near the soft edge Universality in invariant random-matrix models: Existence near the soft edge

1997-01-05

arxiv.org/abs/chao-dyn/9701005v1

Physical Review E 55, 3712 (1997)

Physics

Condensed Matter

Statistical Mechanics

4 pages (revtex), to appear in Physical Review E

Scientific paper

10.1103/PhysRevE.55.3712

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 Gaussian unitary ensemble. This suggests that the invariant one-matrix models should display universal eigenvalue correlations in the soft-edge scaling limit.

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