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Large Random Matrices: Lectures on Macroscopic Asymptotics

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Cover of 'Large Random Matrices: Lectures on Macroscopic Asymptotics'

Table of Contents

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    Book Overview
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    Chapter 1 Introduction
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    Chapter 2 Wigner’s theorem
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    Chapter 3 Wigner's matrices; more moments estimates
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    Chapter 4 Words in several independent Wigner matrices
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    Chapter 5 Concentration inequalities and logarithmic Sobolev inequalities
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    Chapter 6 Generalizations
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    Chapter 7 Concentration inequalities for random matrices
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    Chapter 8 Maps and Gaussian calculus
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    Chapter 9 First-order expansion
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    Chapter 10 Second-order expansion for the free energy
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    Chapter 11 Large deviations for the law of the spectral measure of Gaussian Wigner's matrices
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    Chapter 12 Large Deviations of the Maximum Eigenvalue
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    Chapter 13 Stochastic analysis for random matrices
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    Chapter 14 Large deviation principle for the law of the spectral measure of shifted Wigner matrices
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    Chapter 15 Asymptotics of Harish-Chandra-Itzykson-Zuber integrals and of Schur polynomials
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    Chapter 16 Asymptotics of some matrix integrals
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    Chapter 17 Free probability setting
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    Chapter 18 Freeness
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    Chapter 19 Free entropy
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    Chapter 20 Basics of matrices
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    Chapter 21 Basics of probability theory
Attention for Chapter 9: First-order expansion
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