Large Random Matrices: Lectures on Macroscopic Asymptotics École d'ẗØ de ProbabilitØs de Saint-Flour XXXVI ¿ 2006 /

• Main Author: Guionnet, Alice. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Lecture Notes in Mathematics, 1957
• Subjects: Mathematics.; Matrix theory.; Functional analysis.; Combinatorics.; Distribution (Probability theory).; Functional Analysis.; Probability Theory and Stochastic Processes.; Linear and Multilinear Algebras, Matrix Theory.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-540-69897-5

Random matrix theory has developed in the last few years, in connection with various fields of mathematics and physics. These notes emphasize the relation with the problem of enumerating complicated graphs, and the related large deviations questions. Such questions are also closely related with the...

Table of Contents:

• Notation
• Introduction
• Part I Wigner matrices and moments estimates
• Part II Wigner matrices and concentration inequalities
• Part III Matrix models
• Part IV Eigenvalues of Gaussian Wigner matrices and large deviations
• Part V Stochastic Calculus
• Part VI Free probability
• Part VII Appendix
• References
• Index.