The stochastic block model (SBM) is a random graph model with planted clusters. It is widely
employed as a canonical model to study clustering and community detection, and provides …

This is a tutorial on some basic non-asymptotic methods and concepts in random matrix
theory. The reader will learn several tools for the analysis of the extreme singular values of …

The theory of random matrices plays an important role in many areas of pure mathematics
and employs a variety of sophisticated mathematical tools (analytical, probabilistic and …

The field of random matrix theory has seen an explosion of activity in recent years, with
connections to many areas of mathematics and physics. However, this makes the current …

From social networks such as Facebook, the World Wide Web and the Internet, to the
complex interactions between proteins in the cells of our bodies, we constantly face the …

But, perhaps, we should start with a few words about graphs in general. They are, of course,
one of the prime objects of study in Discrete Mathematics. However, graphs are among the …

This is a study of the universality of spectral statistics for large random matrices. Considered
are symmetric, Hermitian, or quaternion self-dual random matrices with independent …

Consider the problem of estimating the entries of a large matrix, when the observed entries
are noisy versions of a small random fraction of the original entries. This problem has …

We introduce a new notion of graph sparsification based on spectral similarity of graph
Laplacians: spectral sparsification requires that the Laplacian quadratic form of the sparsifier …

A major component of overfitting in model-free reinforcement learning (RL) involves the case
where the agent may mistakenly correlate reward with certain spurious features from the …