Gaussian fluctuations for linear spectral statistics of Wigner beta ensembles
classification
🧮 math.PR
keywords
wignerbetaensemblesstatisticsfluctuationsgaussianlinearmatrices
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As an important topic in Mathematical Physics and statistics, random matrices theory has found uses in many aspects of modern physics and multivariate analysis. This paper is to investigate the Gaussian fluctuations for linear spectral statistics (LSS) of Wigner beta ensembles. We first establish a central limit theorem (CLT) for LSS of Wigner quaternion matrices, then give a general CLT for Wigner $\beta$ ensembles.
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