Asymptotics of level-spacing distributions for random matrices. (English) Zbl 0968.82501
Phys. Rev. Lett. 69, No. 1, 5-8 (1992); errata 69, No. 19, 2880 (1992).
Summary: Asymptotic formulas for the probability of finding exactly \(n\) eigenvalues in an interval of length \(s\), for large \(s\) and fixed \(n\), are given for random matrices taken from the Gaussian ensembles \((\beta =1,2,4)\). These exact results are compared with the predictions of a continuum Coulomb gas model due to Dyson.
MSC:
| 82B05 | Classical equilibrium statistical mechanics (general) |
| 82B10 | Quantum equilibrium statistical mechanics (general) |
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