18 citations · 18 across the 8 of their papers we have counts for
10 papers
Convexity, the spectrum of free Laplacians and geometric consequences: a free KLS bound
Charles-Philippe Diez
We establish a compactness theorem for the resolvent of free Laplacians. More precisely, let be a self-adjoint tuple admitting Lipschitz conjugate variables in…
A tail bound for multi-matrix models with Lipschitz interaction
Charles-Philippe Diez, David Jekel
We give non-asymptotic operator-norm tail bounds for random multi-matrix models with quadratic plus globally Lipschitz interactions. More precisely, let be the probability me…
Obata's rigidity theorem in free probability
Charles-Philippe Diez
We establish a free analogue of Obata's rigidity theorem. More precisely, Cheng and Zhou (2017) proved that on a weighted Riemannian manifold, the sharp spectral gap (Poincaré cons…
Mathematical research with GPT-5: a Malliavin-Stein experiment
Charles-Philippe Diez, Luis da Maia, Ivan Nourdin
On August 20, 2025, GPT-5 was reported to have solved an open problem in convex optimization. Motivated by this episode, we conducted a controlled experiment in the Malliavin--Stei…
Free Stein Kernel and Moments maps
Charles-Philippe Diez
In this paper, we propose a free analogue to Fathi's construction of Stein kernels using moment maps (2019). This is possible for a class of measures called free moment measures th…
A sharp symmetrized free transport-entropy inequality for the semicircular law
Charles-Philippe Diez
In this paper, following the recent work of Fathi (2018) in the classical case, we provide by two different methods a sharp symmetrized free Talagrand inequality for the semicircul…
Free Stein kernels, free moment maps, and higher order derivatives
Charles-Philippe Diez
In this work, we describe new constructions of free Stein kernels. Firstly, in dimension one, we propose a free analog to the construction of Stein kernels using moment maps as the…
Sobolev-Wigner spaces
Charles-Philippe Diez
In this paper, we provide new results about the free Malliavin calculus on the Wigner space first developed in the breakthrough work of Biane and Speicher. We define in this way th…
Free Malliavin-Stein-Dirichlet method: multidimensional semicircular approximations and chaos of a quantum Markov operator
Charles-Philippe Diez
We combine the notion of free Stein kernel and the free Malliavin calculus to provide quantitative bounds under the free (quadratic) Wasserstein distance in the multivariate semici…
Limiting behavior of large correlated Wishart matrices with chaotic entries
Solesne Bourguin, Charles-Philippe Diez, Ciprian A. Tudor
We study the fluctuations, as , of the Wishart matrix associated to a random ma…