Random Matrices

High Dimensional Phenomena

von Gordon Blower

448 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

This book focuses on the behaviour of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups and probability measures in a style suitable for applications in random matrix theory. Later chapters use modern convexity theory to establish subtle results about the convergence of eigenvalue distributions as the size of the matrices increases. Random matrices are viewed as geometrical objects with large dimension. The book analyzes the concentration of measure phenomenon, which describes how measures behave on geometrical objects with large dimension. To prove such results for random matrices, the book develops the modern theory of optimal transportation and proves the associated functional inequalities involving entropy and information. These include the logarithmic Sobolev inequality, which measures how fast some physical systems converge to equilibrium.

• Themen: Mathematik und Naturwissenschaften Mathematik Wahrscheinlichkeitsrechnung und Statistik
• ISBN: 9780521133128
• Sprache: Englisch
• Erscheinungsdatum: 08.10.2009
• Größe: 229 x 152 mm
• Verlag: Cambridge University Press