Lectures on Random Matrices

Random matrices are cool! In this book, the author gives an idea why random matrices are so fascinating and have become a centerpiece of modern mathematics. This book is an introduction to random matrix theory, giving an impression of some of the most important aspects of this modern subject. In particular, it covers the basic combinatorial and analytic theory around Wigner's semicircle law, also featuring concentration phenomena, and the Tracy-Widom distribution of the largest eigenvalue. The circular law and a discussion of Voiculescu's multivariate extension of the semicircle law, as an appetizer for free probability theory, also make an appearance. This book is based on a lecture series for graduate and advanced undergraduate students at Saarland University, Germany.

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