TY - BOOK ID - 4795091 TI - Spectral analysis of large dimensional random matrices AU - Bai, Zhidong. AU - Silverstein, Jack W. PY - 2010 SN - 9781441906618 9781441906601 1441906606 1441906614 1441906622 PB - New York : Springer, DB - UniCat KW - Statistics. KW - Statistical Theory and Methods. KW - Mathematical statistics. KW - Statistique KW - Statistique mathématique KW - Random matrices. KW - Spectrum analysis. KW - Analysis, Spectrum KW - Spectra KW - Spectrochemical analysis KW - Spectrochemistry KW - Spectroscopy KW - Chemistry, Analytic KW - Interferometry KW - Optics KW - Radiation KW - Wave-motion, Theory of KW - Absorption spectra KW - Light KW - Spectroscope KW - Matrices, Random KW - Matrices KW - Qualitative KW - Mathematics. KW - Random matrices KW - Spectrum analysis KW - Algebra KW - Mathematical Statistics KW - Mathematics KW - Physical Sciences & Mathematics KW - Matrices. KW - Algebra, Matrix KW - Cracovians (Mathematics) KW - Matrix algebra KW - Matrixes (Algebra) KW - Algebra, Abstract KW - Algebra, Universal KW - Statistical inference KW - Statistics, Mathematical KW - Statistics KW - Probabilities KW - Sampling (Statistics) KW - Statistical methods KW - Spectrometry KW - Statistics . KW - Statistical analysis KW - Statistical data KW - Statistical science KW - Econometrics KW - Analytical chemistry UR - https://www.unicat.be/uniCat?func=search&query=sysid:4795091 AB - The aim of the book is to introduce basic concepts, main results, and widely applied mathematical tools in the spectral analysis of large dimensional random matrices. The core of the book focuses on results established under moment conditions on random variables using probabilistic methods, and is thus easily applicable to statistics and other areas of science. The book introduces fundamental results, most of them investigated by the authors, such as the semicircular law of Wigner matrices, the Marcenko-Pastur law, the limiting spectral distribution of the multivariate F matrix, limits of extreme eigenvalues, spectrum separation theorems, convergence rates of empirical distributions, central limit theorems of linear spectral statistics, and the partial solution of the famous circular law. While deriving the main results, the book simultaneously emphasizes the ideas and methodologies of the fundamental mathematical tools, among them being: truncation techniques, matrix identities, moment convergence theorems, and the Stieltjes transform. Its treatment is especially fitting to the needs of mathematics and statistics graduate students and beginning researchers, having a basic knowledge of matrix theory and an understanding of probability theory at the graduate level, who desire to learn the concepts and tools in solving problems in this area. It can also serve as a detailed handbook on results of large dimensional random matrices for practical users. This second edition includes two additional chapters, one on the authors' results on the limiting behavior of eigenvectors of sample covariance matrices, another on applications to wireless communications and finance. While attempting to bring this edition up-to-date on recent work, it also provides summaries of other areas which are typically considered part of the general field of random matrix theory. Zhidong Bai is a professor of the School of Mathematics and Statistics at Northeast Normal University and Department of Statistics and Applied Probability at National University of Singapore. He is a Fellow of the Third World Academy of Sciences and a Fellow of the Institute of Mathematical Statistics. Jack W. Silverstein is a professor in the Department of Mathematics at North Carolina State University. He is a Fellow of the Institute of Mathematical Statistics. . ER -