Preface
Acknowledgments
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 centrallimit 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．Related articles
3．1．Brownian motion and Dyson Brownian motion
3．2．The Golden-Thompson inequality
3．3．The Dyson and Airy kernels of GUE via semiclassical analysis
3．4．The mesoscopic structure of GUE eigenvalues
Bibliography
Index
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