Large Random Matrices: Lectures on Macroscopic Asymptotics
École d'Été de Probabilités de Saint-Flour XXXVI, 2006
(Sprache: Englisch)
These lectures emphasize the relation between the problem of enumerating complicated graphs and the related large deviations questions. Such questions are closely related with the asymptotic distribution of matrices.
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These lectures emphasize the relation between the problem of enumerating complicated graphs and the related large deviations questions. Such questions are closely related with the asymptotic distribution of matrices.
Klappentext zu „Large Random Matrices: Lectures on Macroscopic Asymptotics “
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 asymptotic distribution of matrices, which is naturally defined in the context of free probability and operator algebra.
The material of this volume is based on a series of nine lectures given at the Saint-Flour Probability Summer School 2006. Lectures were also given by Maury Bramson and Steffen Lauritzen.
Inhaltsverzeichnis zu „Large Random Matrices: Lectures on Macroscopic Asymptotics “
- Wigner matrices and moments estimates- Wigner’s theorem
- Wigner's matrices; more moments estimates
- Words in several independent Wigner matrices
- Wigner matrices and concentration inequalities
- Concentration inequalities and logarithmic Sobolev inequalities
- Generalizations
- Concentration inequalities for random matrices
- Matrix models
- Maps and Gaussian calculus
- First-order expansion
- Second-order expansion for the free energy
- Eigenvalues of Gaussian Wigner matrices and large deviations
- Large deviations for the law of the spectral measure of Gaussian Wigner's matrices
- Large Deviations of the Maximum Eigenvalue
- Stochastic calculus
- Stochastic analysis for random matrices
- Large deviation principle for the law of the spectral measure of shifted Wigner matrices
- Asymptotics of Harish-Chandra-Itzykson-Zuber integrals and of Schur polynomials
- Asymptotics of some matrix integrals
- Free probability
- Free probability setting
- Freeness
- Free entropy
- Basics of matrices
- Basics of probability theory
Bibliographische Angaben
- Autor: Alice Guionnet
- 2009, 2009, 294 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer
- ISBN-10: 3540698965
- ISBN-13: 9783540698968
- Erscheinungsdatum: 25.03.2009
Sprache:
Englisch
Rezension zu „Large Random Matrices: Lectures on Macroscopic Asymptotics “
From the reviews:"This book is a set of lecture notes on eigenvalues of large random matrices. ... useful to all mathematicians and statisticians who are interested in Wigner matrices. ... In summary, the book is very much worth perusal." (Vladislav Kargin, Mathematical Reviews, Issue 2010 d)
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