Central limit theorem for linear spectral statistics of large dimensional quaternion sample covariance matrices

Laguerre (Wishart) -ensembles, where (known as Dyson's threefold way) are important in Random Matrix Theory. These classical matrices models have been considered by many authors. In this paper, we investigate the central limit theorem for linear spectral statistics of large dimensional quaternion sample covariance matrices, which include the Wishart quaternion ensembles as a special case. Combining with existing results, a general central limit theorem, where are parameters in the expressions of limit mean and variance, is also given.