  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.
