We consider the problem of estimating a large rank‐one tensor u⊗ k∈(ℝn)⊗ k, k≥ 3, in
Gaussian noise. Earlier work characterized a critical signal‐to‐noise ratio λ Bayes= O (1) …

In this paper, we investigate the asymptotic spectrum of complex or real Deformed Wigner
matrices (MN) N defined by M_N=W_N/N+A_N where WN is an N× N Hermitian (resp …

This paper introduces a unified framework for the detection of a single source with a sensor
array in the context where the noise variance and the channel between the source and the …

We study the algorithmic thresholds for principal component analysis of Gaussian k-tensors
with a planted rank-one spike, via Langevin dynamics and gradient descent. In order to …

This paper addresses the problem of reconstructing a low-rank signal matrix observed with
additive Gaussian noise. We first establish that, under mild assumptions, one can restrict …

We study the asymptotic behavior of the spectrum of a random matrix where a non-linearity
is applied entry-wise to a Wigner matrix perturbed by a rank-one spike with independent and …

We give simple criteria to identify the exponential order of magnitude of the absolute value of
the determinant for wide classes of random matrix models, not requiring the assumption of …

Nous étudions la distribution des valeurs propres qui sortent de l'amas du spectre de
matrices de Wigner deformées par une matrice de rang fini sous l'hypothèse que les valeurs …

We present a method to obtain the average and the typical value of the number of critical
points of the empirical risk landscape for generalized linear estimation problems and …

Random matrix theory has developed in the last few years, in connection with various fields
of mathematics and physics. These notes emphasize the relation with the problem of …