Decorrelation in Local Statistics for random operators
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909336781979648 |
|---|---|
| author | Krishna, M. |
| author_facet | Krishna, M. |
| contents | In this paper we study the local spectral statistics in the localised region of various random operator models, including the $d$-dimensional the Anderson model and random Schrödinger operators. It is already established, in the above models, that at an energy $E$, in the localised energy region of the spectrum, where the density of states $n(E) > 0$, the local eigenvalue statistics $X_E$ is a Poisson processes with intensity $n(E) \mathcal{L}$, $\mathcal{L}$ being the Lebesgue measure on $\mathbb{R}$. The question of independence of $X_E, X_{E^\prime}$ for distinct energies was partially solved in the literature. We solve it completely for all the models for which the Minami technique works. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16389 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decorrelation in Local Statistics for random operators Krishna, M. Spectral Theory Mathematical Physics In this paper we study the local spectral statistics in the localised region of various random operator models, including the $d$-dimensional the Anderson model and random Schrödinger operators. It is already established, in the above models, that at an energy $E$, in the localised energy region of the spectrum, where the density of states $n(E) > 0$, the local eigenvalue statistics $X_E$ is a Poisson processes with intensity $n(E) \mathcal{L}$, $\mathcal{L}$ being the Lebesgue measure on $\mathbb{R}$. The question of independence of $X_E, X_{E^\prime}$ for distinct energies was partially solved in the literature. We solve it completely for all the models for which the Minami technique works. |
| title | Decorrelation in Local Statistics for random operators |
| topic | Spectral Theory Mathematical Physics |
| url | https://arxiv.org/abs/2405.16389 |