The Spectral Analysis Of Two Class Of Random Matrices With Dependent Entries

With the development of the society, the high dimensional data begin to appear in people’s life. We often use dimension reduction method for solving high dimensional data analysis problems, which is this method tend to lose mass information contained in the original data. For high dimensional data spectrum analysis is one of the most important methods for high dimensional data, the semicircle law and Marcenko-Pastar(MP)law are two basic conclusions in the spectral analysis of two class of random Matrices.Based on [5] and [2], We prove that the empirical spectral distribution of a class of random matrix with local dependent entries converges to semicircle law, and the empirical spectral distribution of the sample covariance matrix converges to MP law.Refered to [7], we also consider the limiting spectral distribution of the sample covariance matrix with m dependent entries. When the size of the sample n and the dimension of random variable p have the following relation thatp nâ†' 0, the paper discusses the issue of the limiting spectral distribution of the matrix, in terms of two conditions about m is bounded and m is unbounded.