A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York
University This book is a concise and self-contained introduction of recent techniques to …

We consider N× N random matrices of the form H= W+ V where W is a real symmetric
Wigner matrix and V a random or deterministic, real, diagonal matrix whose entries are …

The stochastic block model is a popular tool for studying community structures in network
data. We develop a goodness-of-fit test for the stochastic block model. The test statistic is …

We develop a new method for deriving local laws for a large class of random matrices. It is
applicable to many matrix models built from sums and products of deterministic or …

We consider sample covariance matrices of the form X^*X, where X is an M*N matrix with
independent random entries. We prove the isotropic local Marchenko-Pastur law, ie we …

We introduce a class of M * MM× M sample covariance matrices QQ which subsumes and
generalizes several previous models. The associated population covariance matrix Σ= EQ …

We consider large non-Hermitian N× N matrices with an additive independent, identically
distributed (iid) noise for each matrix elements. We show that already a small noise of …

Graph matching, also known as network alignment, aims at recovering the latent vertex
correspondence between two unlabeled, edge-correlated weighted graphs. To tackle this …

We consider the local eigenvalue distribution of large self-adjoint N * NN× N random
matrices H= H^* H= H∗ with centered independent entries. In contrast to previous works the …

We consider large random matrices with a general slowly decaying correlation among its
entries. We prove universality of the local eigenvalue statistics and optimal local laws for the …