极限周期介质中的均匀安德森定位和非局部迷你型估算

IF 0.4 4区数学 Q4 STATISTICS & PROBABILITY Markov Processes and Related Fields Pub Date : 2024-01-02 DOI:10.61102/1024-2953-mprf.2023.29.4.004

V. Chulaevsky, Y. Suhov

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引用次数: 0

摘要

我们证明了一类极限周期晶格施罗丁格算子的特征函数均匀指数定位和谱的简单性。证明的一个重要成分是著名的南估计（特征值的相关不等式）的广义变体，它适用于谱区间可以任意置于实线上的情况。新的相关不等式使我们能够大幅简化 KAM（Kolmogorov-Arnold-Moser）技术的应用，并使其更加透明。

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Uniform Anderson Localization and Non-local Minami-type Estimates in Limit-periodic Media

We prove a uniform exponential localization of eigenfunctions and simplicity of spectrum for a class of limit-periodic lattice Schr¨odinger operators. An important ingredient of the proof is a generalized variant of the well-known Minami estimates (correlation inequalities for the eigenvalues) to the case where the spectral intervals can be arbitrarily placed in the real line. The new corre- lation inequalities allow us to substantially simplify and make more transparent the application of the KAM (Kolmogorov-Arnold-Moser) techniques.

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来源期刊

Markov Processes and Related Fields STATISTICS & PROBABILITY-

CiteScore

0.70

自引率

0.00%

发文量

期刊介绍： Markov Processes And Related Fields The Journal focuses on mathematical modelling of today''s enormous wealth of problems from modern technology, like artificial intelligence, large scale networks, data bases, parallel simulation, computer architectures, etc. Research papers, reviews, tutorial papers and additionally short explanations of new applied fields and new mathematical problems in the above fields are welcome.