This review covers recent results concerning the estimation of large covariance matrices
using tools from Random Matrix Theory (RMT). We introduce several RMT methods and …

Extreme value statistics (EVS) concerns the study of the statistics of the maximum or the
minimum of a set of random variables. This is an important problem for any time-series and …

The past two decades have seen transformative advances in cosmology and string theory.
Observations of the cosmic microwave background have revealed strong evidence for …

We study the fluctuations of the largest eigenvalue λ max of N× N random matrices in the
limit of large N. The main focus is on Gaussian β ensembles, including in particular the …

We consider the phase retrieval problem of reconstructing a $ n $-dimensional real or
complex signal $\mathbf {X}^\star $ from $ m $(possibly noisy) observations $ Y_\mu=|\sum …

We calculate the average number of critical points of a Gaussian field on a high-dimensional
space as a function of their energy and their index. Our results give a complete picture of the …

We compute exact asymptotic results for the probability of the occurrence of large deviations
of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian …

Heterogeneous diffusion with a spatially changing diffusion coefficient arises in many
experimental systems such as protein dynamics in the cell cytoplasm, mobility of cajal …

The big-jump principle is a well-established mathematical result for sums of independent
and identically distributed random variables extracted from a fat-tailed distribution. It states …

We consider an infinite system of particles on a line performing identical Brownian motions
and interacting through the| x− y|− s Riesz potential, causing the overdamped motion of …