Introduction to Random Matrices - Theory and Practice

Abstract

This is a book for absolute beginners. If you have heard about random matrix theory, commonly denoted RMT, but you do not know what that is, then welcome!, this is the place for you. Our aim is to provide a truly accessible introductory account of RMT for physicists and mathematicians at the beginning of their research career. We tried to write the sort of text we would have loved to read when we were beginning Ph.D. students ourselves. Our book is structured with light and short chapters, and the style is informal. The calculations we found most instructive are spelt out in full. Particular attention is paid to the numerical verification of most analytical results. Our book covers standard material - classical ensembles, orthogonal polynomial techniques, spectral densities and spacings - but also more advanced and modern topics - replica approach and free probability - that are not normally included in elementary accounts on RMT. This book is dedicated to the fond memory of Oriol Bohigas.

References in corpus (3)

• Extreme Eigenvalues of Wishart Matrices: Application to Entangled Bipartite System
• Symmetry classes in random matrix theory
• Matrix integrals and enumeration of maps

Cited by in corpus (4)

• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Capacity-resolution trade-off in the optimal learning of multiple low-dimensional manifolds by attractor neural networks
• Statistically related many-body localization in the one-dimensional anyon Hubbard model
• From entropic to energetic barriers in glassy dynamics: The Barrat-Mézard trap model on sparse networks