Some asymptotic properties of the spectrum of the Jacobi ensemble
| dc.creator | Dette, Holger | |
| dc.creator | Nagel, Jan | |
| dc.date | 2009-04-27 | |
| dc.date.accessioned | 2026-07-07T13:08:55Z | |
| dc.date.available | 2026-07-07T13:08:55Z | |
| dc.description | For the random eigenvalues with density corresponding to the Jacobi ensemble $$c \cdot \prod_{i < j} | λ_i - λ_j |^β\prod^n_{i=1} (2 - λ_i)^a (2 + λ_i)^b I_{(-2,2)} (λ_i) $$ $(a, b > -1, β> 0) $ a strong uniform approximation by the roots of the Jacobi polynomials is derived if the parameters $a, b,$ $β$ depend on $n$ and $n \to \infty$. Roughly speaking, the eigenvalues can be uniformly approximated by roots of Jacobi polynomials with parameters $((2a+2)/β-1, (2b+2)/β-1)$, where the error is of order $\{\log n/(a+b) \}^{1/4}$. These results are used to investigate the asymptotic properties of the corresponding spectral distribution if $n \to \infty$ and the parameters $a, b$ and $β$ vary with $n$. We also discuss further applications in the context of multivariate random $F$-matrices. | |
| dc.description | 20 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/0904.4091 | |
| dc.identifier | http://arxiv.org/abs/0904.4091 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228572 | |
| dc.subject | Probability | |
| dc.subject | 60F15 (Primary); 15A52 (Secondary) | |
| dc.title | Some asymptotic properties of the spectrum of the Jacobi ensemble | |
| dc.type | text |