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 …

We survey here some recent studies concerning what we call mean-field models by analogy
with Statistical Mechanics and Physics. More precisely, we present three examples of our …

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 …

We consider integrals on unitary groups U d of the form ?U_dU_i_1?j_1⋯U_i_q?j_qU_j^'_1i
^'_1^∗⋯U_j^'_q^'i^'_q^'^∗dU. We give an explicit formula in terms of characters of …

One of the most important properties of neural networks is the clustering of local minima of
the loss function near the global minimum, enabling efficient training. Though generative …

The macroscopic fluctuation theory (MFT) is an effective framework to describe transports
and their fluctuations in classical out-of-equilibrium diffusive systems. Whether the MFT may …

We consider the additive version of the matrix denoising problem, where a random
symmetric matrix S of size n has to be inferred from the observation of Y= S+ Z, with Z an …

Résumé Nous poursuivons dans cette Note notre étude de la notion de jeux à champ
moyen introduite dans une Note précédente. Nous considérons ici le cas d'équilibres de …

Factorization of matrices where the rank of the two factors diverges linearly with their sizes
has many applications in diverse areas such as unsupervised representation learning …

We consider increasingly complex models of matrix denoising and dictionary learning in the
Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank …