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Random matrix theory

Random matrix theory

Chapter 1. Preparatory material §1.1.A review of probability theory §1.2.Stirling's formula §1.3.Eigenvalues and sums of Hermitian matrices Chapter 2. Random matrices §2.1.Concentration of measure §2.2.The central limit theorem §2.3.The operator norm of random matrices §2.4.The semicircular law §2.5.Free probability §2.6.Gaussian ensembles §2.7.The least singular value §2.8.The circular law Chapter 3. …