4 papers
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 con…
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…
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 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…