Journée du GDR MEGA

Contribution List

2. Interpolation between random matrices and free operators.

Parraud Félix

2/17/23, 10:30 AM

We shall start by introducing the problems that this method was first designed to solve, notably the question of strong convergence of a family of random matrices. Indeed if one considers a polynomial in those random matrices, one can wonder how the spectrum of the resulting matrix behaves when the dimension goes to infinity. In particular, a recurring question is whether the operator norm...

1. Colloquium : Sur la théorie conforme des champs de Liouville (Amphi Schwartz)

Colin Guillarmou

2/17/23, 2:00 PM

Les théories conformes des champs en dimension 2 sont apparues en physique
dans les années 80 pour décrire certaines limites d’échelles de modèles de physique statistique, comme Ising par exemple. Il s’agit de théories quantiques des champs particulières : elles contiennent de nombreuses symétries, les transformations conformes locales, et peuvent être parfois résolues par des outils de...

3. Estimation of (I_n - XDX^T)^{-1} with large dependence and concentration hypotheses.

Cosme Louart

2/17/23, 3:30 PM

We provide in this presentation an estimation of the expectation of the matrix Q(D) = (I_p - XDX^T)^{-1} when the data matrix X = (x_1, ...,x_n) \in M_{p,n} has independent columns (but not identically distributed) and D is random, bounded, not independent with X but satisfies some constraints on the dependence on each x_i: for any i, there exists a random diagonal matrix D_i independent of...