Recent progress in combinatorial random matrix theory Page 1 Probability Surveys Vol. 18 (2021)
179–200 ISSN: 1549-5787 https://doi.org/10.1214/20-PS346 Recent progress in combinatorial …

Sparse linear regression is a fundamental problem in high-dimensional statistics, but
strikingly little is known about how to efficiently solve it without restrictive conditions on the …

Two landmark results in combinatorial random matrix theory, due to Koml\'os and Costello-
Tao-Vu, show that discrete random matrices and symmetric discrete random matrices are …

We develop a unified approach to bounding the largest and smallest singular values of an
inhomogeneous random rectangular matrix, based on the non-backtracking operator and …

Let ξ ξ be a non-constant real-valued random variable with finite support and let M_ n (ξ) M n
(ξ) denote an n * nn× n random matrix with entries that are independent copies of ξ ξ. For ξ ξ …

Sparse linear regression with ill-conditioned Gaussian random covariates is widely believed
to exhibit a statistical/computational gap, but there is surprisingly little formal evidence for …

The problem of estimating the smallest singular value of random square matrices is
important in connection with matrix computations and analysis of the spectral distribution. In …

Consider a random symmetric matrix with iid~ entries on and above its diagonal that are
products of Bernoulli random variables and random variables with sub-Gaussian tails. Such …

Very sparse random graphs are known to typically be singular (ie, have singular adjacency
matrix) due to the presence of “low-degree dependencies” such as isolated vertices and …

Sparse linear regression with ill-conditioned Gaussian random designs is widely believed to
exhibit a statistical/computational gap, but there is surprisingly little formal evidence for this …