Lectures on Random Matrices

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