In the setting of generic β-ensembles, we use the loop equation hierarchy to prove a local
law with optimal error up to a constant, valid on any scale including microscopic. This local …

Statistical inference for principal components of spiked covariance matrices Page 1 The Annals
of Statistics 2022, Vol. 50, No. 2, 1144–1169 https://doi.org/10.1214/21-AOS2143 © Institute of …

We consider inhomogeneous Erdős–Rényi graphs. We suppose that the maximal mean
degree d satisfies d≪ log n. We characterise the asymptotic behaviour of the n 1–o (1) …

We consider large non-Hermitian real or complex random matrices XX with independent,
identically distributed centred entries. We prove that their local eigenvalue statistics near the …

We complete the analysis of the extremal eigenvalues of the adjacency matrix A of the Erdős–
Rényi graph G (N, d/N) in the critical regime d≍ log N of the transition uncovered in (Ann …

We prove local laws, ie optimal concentration estimates for arbitrary products of resolvents of
a Wigner random matrix with deterministic matrices in between. We find that the size of such …

Singular vector and singular subspace distribution for the matrix denoising model Page 1
The Annals of Statistics 2021, Vol. 49, No. 1, 370–392 https://doi.org/10.1214/20-AOS1960 © …

Single-cell technologies provide the opportunity to identify new cellular states. However, a
major obstacle to the identification of biological signals is noise in single-cell data. In …

We survey recent mathematical results about the spectrum of random band matrices. We
start by exposing the Erdős–Schlein–Yau dynamic approach, its application to Wigner …

We consider the statistics of the extreme eigenvalues of sparse random matrices, a class of
random matrices that includes the normalized adjacency matrices of the Erd {\H o} sR {\'e} …