Multi-dimensional Semicircular Limits on the Free Wigner Chaos

机译：免费的Wigner混乱上的多维半圆形限制

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We show that, for sequences of vectors of multiple Wigner integrals with respect to a free Brownian motion, componentwise convergence to semicircular law is equivalent to joint convergence. This result extends to the free probability setting some findings by Peccati and Tudor (2005), and represents a multi-dimensional counterpart of a limit theorem inside the free Wigner chaos established by Kemp, Nourdin, Peccati and Speicher (2011).

机译：我们表明，对于多个Wigner的序列相对于自由褐色运动，对半周法的组成方向收敛相当于关节会聚。该结果延伸到Peccati和Tudor（2005）的自由概率设置一些发现，并且代表了Kemp，Nourdin，Peccati和Speicher（2011）建立的免费Wigner混沌内的极限定理的多维对应物。

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《Seminar on Stochastic Analysis, Random Fields, and Applications》|2013年||共11页
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作者
Ivan Nourdin; Giovanni Peccati; Roland Speicher;
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原文格式 PDF
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中图分类 O211.6-532;
关键词
Convergence in distribution; fourth moment condition; free Brownian motion; free probability; multi-dimensional limit theorems; semicircular law; Wigner chaos;

机译：分布融合;第四个时刻条件;自由布朗运动;自由概率;多维限制定理;半核法;Wigner Chaos;

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1. Semicircular limits on the free Poisson chaos:Counterexamples to a transfer principle [J] . Solesne Bourguin, Giovanni Peccati Journal of Functional Analysis . 2014,第4期

机译：自由泊松混沌的半圆极限：转移原理的反例
2. Free Convolution with a Semicircular Distribution and Eigenvalues of Spiked Deformations of Wigner Matrices [J] . Capitaine Mireille, Donati-Martin Catherine, Féral Delphine, Electronic Journal of Probability . 2011,第45a48期

机译：具有Wigner矩阵的尖峰变形的半圆分布和特征值的自由卷积
3. Poisson approximations on the free wigner chaos [J] . Nourdin I., Peccati G. The Annals of Probability: An Official Journal of the Institute of Mathematical Statistics . 2013,第4期

机译：自由维格纳混沌中的泊松近似
4. Multi-dimensional Semicircular Limits on the Free Wigner Chaos [C] . Ivan Nourdin, Giovanni Peccati, Roland Speicher Seminar on Stochastic Analysis, Random Fields, and Applications . 2013

机译：免费的Wigner混乱上的多维半圆形限制
5. The Central Limit Theorem for Linear Spectral Statistics of Submatrices of the Gaussian Wigner Random Matrices [D] . Reed, Matthew. 2014

机译：高斯Wigner随机矩阵的子矩阵线性谱统计的中心极限定理。
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7. Multidimensional semicircular limits on the free Wigner chaos [O] . Nourdin, Ivan, Peccati, Giovanni, Speicher, Roland 2013

机译：对自由Wigner混沌的多维半圆限制

Multi-dimensional Semicircular Limits on the Free Wigner Chaos

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