Spectral Analysis of Large Dimensional Random Matrices - Mathematics Monograph Series 15

The aim of the book is to introduce basic concepts,main results,and widely applied mathematical tools in the spectral analysis of large dimensional ran dom matrices.The core of the book focuses on results established under moment conditions on random variales using probabilistic methods,and is thus easily applicable to statistice and other areas of science.The book introduces fundamental results,most of them invertigated by the authors,such as the semicircular law of Wigner matrices,the Marcenko-Pastur law,the limiting soectral distribution of the multivariate F-matrix,limits of extreme eigenvalues,spectrum separation theorems,convergence rates of emporocal distributions,central limit theorems if linera soectral statistics,and the partial solution of the famous circular law.While deriving the main results,the book simultaneously emphasizes the ideas and methdologies of the fundamental mathematical tools,among them being:truncation techniques,matrix identities,moment convergence theorems,and the Stieltjes tra