Asymptotic eigenvalue distribution of large Toeplitz matrices
| dc.creator | Lee, Seung-Yeop | |
| dc.creator | Dai, Hui | |
| dc.creator | Bettelheim, Eldad | |
| dc.date | 2007-08-23 | |
| dc.date.accessioned | 2026-07-07T08:25:10Z | |
| dc.date.available | 2026-07-07T08:25:10Z | |
| dc.description | We study the asymptotic eigenvalue distribution of Toeplitz matrices generated by a singular symbol. It has been conjectured by Widom that, for a generic symbol, the eigenvalues converge to the image of the symbol. In this paper we ask how the eigenvalues converge to the image. For a given Toeplitz matrix $T_n(a)$ of size $n$, we take the standard approach of looking at $\det(ζ-T_n(a))$, of which the asymptotic information is given by the Fisher-Hartwig theorem. For a symbol with single jump, we obtain the distribution of eigenvalues as an expansion involving $1/n$ and $\log n/n$. To demonstrate the validity of our result we compare our result against the numerics using a pure Fisher-Hartwig symbol. | |
| dc.identifier | https://arxiv.org/abs/0708.3124 | |
| dc.identifier | http://arxiv.org/abs/0708.3124 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136574 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 15A15, 15A18, 15A60, 47B35 | |
| dc.title | Asymptotic eigenvalue distribution of large Toeplitz matrices | |
| dc.type | text |