Lectures on Random Matrices

  • Roland Speicher

    Saarland University, Saarbrücken, Germany
Lectures on Random Matrices cover

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FrontmatterDownload pp. i–iv
PrefaceDownload pp. v–viii
Contents Download pp. ix–xi
1Introductionpp. 1–11
2Gaussian random matrices: Wick formula and combinatorial proof of Wigner’s semicircle lawpp. 13–23
3Wigner matrices: Combinatorial proof of Wigner’s semicircle lawpp. 25–30
4Analytic tools: Stieltjes transform and convergence of measurespp. 31–40
5Analytic proof of Wigner’s semicircle law for Gaussian random matrices pp. 41–47
6Concentration phenomena and stronger forms of convergence for the semicircle lawpp. 49–59
7Analytic description of the eigenvalue distribution of Gaussian random matricespp. 61–72
8Determinantal processes and non-crossing paths: Karlin–McGregor and Gessel–Viennotpp. 73–78
9Statistics of the largest eigenvalue and Tracy–Widom distributionpp. 79–94
10Statistics of the longest increasing subsequencepp. 95–100
11The circular lawpp. 101–106
12Several independent GUEs and asymptotic freenesspp. 107–112
Referencespp. 113–115
Indexpp. 117–119