The matrix Dyson equation and its applications for random matrices

Understand

These lecture notes are a concise introduction of recent techniques to prove local spectral universality for a large class of random matrices.

• The general strategy is presented following the recent book with H.T.
• Yau.
• We extend the scope of this book by focusing on new techniques developed to deal with generalizations of Wigner matrices that allow for non-identically distributed entries and even for correlated entries.