Deviations from the Circular Law
| dc.creator | Rider, Brian | |
| dc.date | 2003-12-01 | |
| dc.date.accessioned | 2026-07-07T05:03:27Z | |
| dc.date.available | 2026-07-07T05:03:27Z | |
| dc.description | Consider Ginibre's ensemble of $N \times N$ non-Hermitian random matrices in which all entries are independent complex Gaussians of mean zero and variance $\frac{1}{N}$. As $N \uparrow \infty$ the normalized counting measure of the eigenvalues converges to the uniform measure on the unit disk in the complex plane. In this note we describe fluctuations about this {\em Circular Law}. First we obtain finite $N$ formulas for the covariance of certain linear statistics of the eigenvalues. Asymptotics of these objects coupled with a theorem of Costin and Lebowitz then result in central limit theorems for a variety of these statistics. | |
| dc.identifier | https://arxiv.org/abs/math/0312043 | |
| dc.identifier | http://arxiv.org/abs/math/0312043 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69424 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.title | Deviations from the Circular Law | |
| dc.type | text |