Large random matrices : lectures on macroscopic asymptotics : École d'Été de Probabilités de Saint-Flour XXXVI-2006
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...
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| Institution som forfatter: | |
| Format: | Livre numérique |
| Sprog: | Anglais |
| Udgivet: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Udgivelse: | 1st ed. 2009. |
| Serier: | École d'Été de Probabilités de Saint-Flour
1957 |
| Fag: | |
| Online adgang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Kommentar: |
Description d'apès consultation du 23 janvier 2012 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Large random matrices, lectures on macroscopic asymptotics, Ecole d'été de probabilités de Saint-Flour XXXVI-2006, Alice Guionnet, Berlin, Springer, 2009, 1 vol. (XII-294 p.), Lecture notes in mathematics, 978-3-540-69896-8 • Large Random Matrices: Lectures on Macroscopic Asymptotics, Texte imprimé, 9783540866107 • Large random matrices, lectures on macroscopic asymptotics, Ecole d'été de probabilités de Saint-Flour XXXVI-2006, Alice Guionnet, Berlin, Springer, 2009, 1 vol. (XII-294 p.), Lecture notes in mathematics, 978-3-540-69896-8 |
Indholdsfortegnelse:
- 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