多维Anderson模型的谱涨落

IF 1 3区数学 Q1 MATHEMATICS

Journal of Spectral Theory Pub Date : 2020-10-18 DOI:10.4171/jst/412

Yoel Grinshpon, Moshe J. White

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引用次数: 0

摘要

在本文中，我们研究了具有有限矩的任何势在$\mathbb｛Z｝^d$上的Anderson模型的多项式线性统计的波动。我们证明，如果用截断算子大小的平方根进行归一化，这些波动会收敛到高斯极限。对于绝大多数势和多项式，我们证明了极限分布的方差是严格正的，并对不发生这种情况的罕见情况进行了全面分类。

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Spectral fluctuations for the multi-dimensional Anderson model

In this paper, we examine fluctuations of polynomial linear statistics for the Anderson model on $\mathbb{Z}^d$ for any potential with finite moments. We prove that if normalized by the square root of the size of the truncated operator, these fluctuations converge to a Gaussian limit. For a vast majority of potentials and polynomials, we show that the variance of the limiting distribution is strictly positive, and we classify in full the rare cases in which this does not happen.

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来源期刊

Journal of Spectral Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

0.00%

发文量

期刊介绍： The Journal of Spectral Theory is devoted to the publication of research articles that focus on spectral theory and its many areas of application. Articles of all lengths including surveys of parts of the subject are very welcome. The following list includes several aspects of spectral theory and also fields which feature substantial applications of (or to) spectral theory. Schrödinger operators, scattering theory and resonances; eigenvalues: perturbation theory, asymptotics and inequalities; quantum graphs, graph Laplacians; pseudo-differential operators and semi-classical analysis; random matrix theory; the Anderson model and other random media; non-self-adjoint matrices and operators, including Toeplitz operators; spectral geometry, including manifolds and automorphic forms; linear and nonlinear differential operators, especially those arising in geometry and physics; orthogonal polynomials; inverse problems.