Saved in:
Bibliographic Details
Main Author: Krishna, M.
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2405.16389
Tags: Add Tag
No Tags, Be the first to tag this record!
_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