Lindeberg Technique And Random Matrix Inequalities

This paper studies and summarizes the application of Lindeberg's technique in ran-dom matrices.By introducing the matrix Stein pairs,combined with the Laplace trans-formation method,it proves some concentration inequalities of random matrices.These inequalities play a very important role in the study of random matrix eigenvalues.The first chapter of this article briefly introduces the Lindeberg method.The second chapter introduces the matrix Stein pairs and Laplace transformation method.The third chapter summarizes the exponential concentration inequalities,and with the help of Lindeberg techniques,derive the matrix Hoeffding and Bernstein inequalities.The fourth chap-ter summarizes the polynomial moment inequalities,and with the help of Lindeberg's technique,derive the matrix Khintchine and Rosenthal inequalities.The fifth chapter gives two non-Hermitian concentration inequalities.