Random matrix theory: A program of the statistics and applied mathematical sciences institute (SAMSI)

Craig Tracy and I became coorganizers and the program's scope was enlarged.It now included regularization issues, inference in graphical models, Bayesian multivariate analysis in such models, applications of random matrix theory particularly in electrical engineering, as well as applications of regularization and high dimensional multivariate analysis in geophysical models.The program was realized as a six-month session in 2006-2007 and featured not only the usual opening workshop at SAMSI but also two closing workshops, one at NCAR (National Center for Atmospheric Research) focused on applications, and one at AIM (American Institute of Mathematics) focused on theory.Two other workshops, one on scoping geophysical models at NCAR and another at SAMSI on Large Graphical Models and Random Matrices, a Bayesian focus week and a course in random matrices also resulted.These activities were supported by an enthusiastic group of postdoctoral fellows, visitors and local faculty and graduate students, as well as a video link for weekly lectures alternating between Berkeley on the West Coast and SAMSI on the East.The Editors of The Annals of Statistics, Susan Murphy and Bernard Silverman, agreed to devote this issue of The Annals of Statistics to exhibit some of the fruits of this program.Papers were submitted and subjected to the normal refereeing procedures.The papers included touch on most of the interests present in the program.Zeitouni and Anderson's paper bridges the gap between Random Matrix Theory and Regularized Estimation by showing that statistics based on the bulk spectrum of regularized empirical covariance matrices behave as one would like them to do.Johnstone extends his powerful limiting result on covariance matrices to canonical correlations, making contributions to both Random Matrix Theory and Statistical Inference.Raj Rao, Mingo, Speicher and Edelman provide novel workable methods and algorithms for testing equality of eigenvalues which are robust in the