Phase transition of the largest eigenvalue for non-null complex sample covariance matrices
| dc.creator | Baik, Jinho | |
| dc.creator | Arous, Gerard Ben | |
| dc.creator | Peche, Sandrine | |
| dc.date | 2004-03-01 | |
| dc.date | 2004-10-21 | |
| dc.date.accessioned | 2026-07-07T05:05:49Z | |
| dc.date.available | 2026-07-07T05:05:49Z | |
| dc.description | We compute the limiting distributions of the largest eigenvalue of a complex Gaussian sample covariance matrix when both the number of samples and the number of variables in each sample become large. When all but finitely many, say $r$, eigenvalues of the covariance matrix are the same, the dependence of the limiting distribution of the largest eigenvalue of the sample covariance matrix on those distinguished $r$ eigenvalues of the covariance matrix is completely characterized in terms of an infinite sequence of new distribution functions that generalize the Tracy-Widom distributions of the random matrix theory. Especially a phase transition phenomena is observed. Our results also apply to a last passage percolation model and a queuing model. | |
| dc.description | 50 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/math/0403022 | |
| dc.identifier | http://arxiv.org/abs/math/0403022 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70314 | |
| dc.subject | Probability | |
| dc.title | Phase transition of the largest eigenvalue for non-null complex sample covariance matrices | |
| dc.type | text |