Large Random Matrices: Lectures on Macroscopic Asymptotics

École d'Été de Probabilités de Saint-Flour XXXVI ¿ 2006

Authors:

ISBN: 978-3-540-69896-8 (Print) 978-3-540-69897-5 (Online)

Table of contents (23 chapters)

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  1. Front Matter

    Pages 1-11

  2. No Access

    Book Chapter

    Pages 1-4

    Introduction

  3. Wigner matrices and moments estimates

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 1-22

      Wigner’s theorem

    3. No Access

      Book Chapter

      Pages 1-12

      Wigner's matrices; more moments estimates

    4. No Access

      Book Chapter

      Pages 1-6

      Words in several independent Wigner matrices

  4. Wigner matrices and concentration inequalities

    1. Front Matter

      Pages 1-2

    2. No Access

      Book Chapter

      Pages 1-9

      Concentration inequalities and logarithmic Sobolev inequalities

    3. No Access

      Book Chapter

      Pages 1-6

      Generalizations

    4. No Access

      Book Chapter

      Pages 1-23

      Concentration inequalities for random matrices

  5. Matrix models

    1. Front Matter

      Pages 1-3

    2. No Access

      Book Chapter

      Pages 1-15

      Maps and Gaussian calculus

    3. No Access

      Book Chapter

      Pages 1-11

      First-order expansion

    4. No Access

      Book Chapter

      Pages 1-25

      Second-order expansion for the free energy

  6. Eigenvalues of Gaussian Wigner matrices and large deviations

    1. Front Matter

      Pages 1-2

    2. No Access

      Book Chapter

      Pages 1-10

      Large deviations for the law of the spectral measure of Gaussian Wigner's matrices

    3. No Access

      Book Chapter

      Pages 1-5

      Large Deviations of the Maximum Eigenvalue

  7. Stochastic calculus

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 1-15

      Stochastic analysis for random matrices

    3. No Access

      Book Chapter

      Pages 1-27

      Large deviation principle for the law of the spectral measure of shifted Wigner matrices

    4. No Access

      Book Chapter

      Pages 1-6

      Asymptotics of Harish-Chandra-Itzykson-Zuber integrals and of Schur polynomials

    5. No Access

      Book Chapter

      Pages 1-8

      Asymptotics of some matrix integrals

  8. Free probability

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 1-4

      Free probability setting

    3. No Access

      Book Chapter

      Pages 1-14

      Freeness

    4. No Access

      Book Chapter

      Pages 1-15

      Free entropy

  9. Appendix

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 1-3

      Basics of matrices

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