Spectral Analysis of Large Dimensional Random Matrices

From the reviews of the second edition: "This book provides an excellent introduction to basic results and methodologies developed on large-dimensional random matrices. The targeted readers are graduate students and researchers who are interested in spectral aspects of RMT and large-dimensional data analysis. The book can also serve as a reference text for practical users. ... The book is organized and written very well, with a wide collection of useful historical notes and references. ... In summary, the book is going to be a classic in the field of RMT."--- (Wenbo V. Li, Mathematical Reviews, Issue 2011 d) "The aim and scope of this edition is to provide upper-level undergraduate students, graduate students, and research workers the understandings and working knowledge of spectral analysis of large-dimensional random matrices ... . it deepens the understanding of applications of random matrices and its applications in finance and engineering. ... an important contribution, providing up-to-date coverage on the general field of random matrix theory in a systematic and logical manner. ... Both graduate students and researchers in this area will find this book handy and helpful." (Technometrics, Vol. 54 (1), February, 2012)

• Wigner Matrices and Semicircular Law.- Sample Covariance Matrices and the Mar#x010D;enko-Pastur Law.- Product of Two Random Matrices.- Limits of Extreme Eigenvalues.- Spectrum Separation.- Semicircular Law for Hadamard Products.- Convergence Rates of ESD.- CLT for Linear Spectral Statistics.- Eigenvectors of Sample Covariance Matrices.- Circular Law.- Some Applications of RMT.