维格纳矩阵最大特征值的小偏差估计

IF 1.5 2区数学 Q2 STATISTICS & PROBABILITY

Bernoulli Pub Date : 2021-12-22 DOI:10.3150/22-bej1490

L'aszl'o ErdHos, Yuanyuan Xu

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引用次数: 3

摘要

我们对实对称和复埃尔米特矩阵的最大特征值建立了精确的右尾小偏差估计，这些矩阵的条目是具有一致有界矩的独立随机变量。该证明依赖于沿长时间连续插值矩阵流的格林函数比较。在左尾部也获得了不太精确的估计。

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Small deviation estimates for the largest eigenvalue of Wigner matrices

We establish precise right-tail small deviation estimates for the largest eigenvalue of real symmetric and complex Hermitian matrices whose entries are independent random variables with uniformly bounded moments. The proof relies on a Green function comparison along a continuous interpolating matrix flow for a long time. Less precise estimates are also obtained in the left tail.

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来源期刊

Bernoulli 数学-统计学与概率论

CiteScore

3.40

自引率

0.00%

发文量

116

审稿时长

6-12 weeks

期刊介绍： BERNOULLI is the journal of the Bernoulli Society for Mathematical Statistics and Probability, issued four times per year. The journal provides a comprehensive account of important developments in the fields of statistics and probability, offering an international forum for both theoretical and applied work. BERNOULLI will publish: Papers containing original and significant research contributions: with background, mathematical derivation and discussion of the results in suitable detail and, where appropriate, with discussion of interesting applications in relation to the methodology proposed. Papers of the following two types will also be considered for publication, provided they are judged to enhance the dissemination of research: Review papers which provide an integrated critical survey of some area of probability and statistics and discuss important recent developments. Scholarly written papers on some historical significant aspect of statistics and probability.