TY - BOOK
AU - Meckes, Elizabeth S.
TI - The random matrix theory of the classical compact groups
PB - New York, NY: Cambridge University Press
PY - 2019
SP - xi, 212 pages
T3 - Cambridge tracts in mathematics ; 218.
AB - This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject's deep connections to geometry, analysis, algebra, physics, and statistics. The book sets a foundation with an introduction to the groups themselves and six different constructions of Haar measure. Classical and recent results are then presented in a digested, accessible form, including the following: results on the joint distributions of the entries; an extensive treatment of eigenvalue distributions, including the Weyl integration formula, moment formulae, and limit theorems and large deviations for the spectral measures; concentration of measure with applications both within random matrix theory and in high dimensional geometry; and results on characteristic polynomials with connections to the Riemann zeta function. This book will be a useful reference for researchers and an accessible introduction for students in related fields.
LA - English
KW - Random matrices
KW - Matrices
SN - 9781108419529
CN - QA196.5 .M43 2019
ER -