圆形β系综光谱测量的量纲结果

IF 1.4 2区数学 Q2 STATISTICS & PROBABILITY

Annals of Applied Probability Pub Date : 2022-12-01 DOI:10.1214/22-aap1798

Tom Alberts, Raoul Normand

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引用次数: 0

摘要

研究了圆形β系综的光谱测度的量纲性质。对于β≥2，如果Simon先前证明了∂D上的Lebesgue测度几乎肯定是奇异连续的，并且它的支持维数为1−2 /β。我们用概率技术和Jitomirskaya-Last不等式的组合来证明这个结果。我们的方法本质上更简单，而且大部分是自包含的，强调概率方面而不是分析方面。我们还扩展了该方法，证明了Jitomirskaya-Last分析中涉及的范数的大偏差原理

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Dimension results for the spectral measure of the circular β ensembles

We study the dimension properties of the spectral measure of the Circular β -Ensembles. For β ≥ 2 it it was previously shown by Simon that the spectral measure is almost surely singular continuous with respect to Lebesgue measure on ∂ D and the dimension of its support is 1 − 2 /β . We reprove this result with a combination of probabilistic techniques and the so-called Jitomirskaya-Last inequalities. Our method is simpler in nature and mostly self-contained, with an emphasis on the probabilistic aspects rather than the analytic. We also extend the method to prove a large deviations principle for norms involved in the Jitomirskaya-Last analysis

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来源期刊

Annals of Applied Probability 数学-统计学与概率论

CiteScore

2.70

自引率

5.60%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The Annals of Applied Probability aims to publish research of the highest quality reflecting the varied facets of contemporary Applied Probability. Primary emphasis is placed on importance and originality.