A Free Stochastic Partial Differential Equation

Yoann Dabrowski (1)

1 PSPM - Probabilités, statistique, physique mathématique

We get stationary solutions of a free stochastic partial differential equation. As an application, we prove equality of non-microstate and microstate free entropy dimensions under a Lipschitz like condition on conjugate variables, assuming also R^\omega\ embeddability. This includes an N-tuple of q-Gaussian random variables e.g. for |q|N\leq 0.13.

Mots clés: Lower bounds on microstate Free Entropy Dimension; Free Stochastic Partial Differential Equations; Free probability; q-Gaussian variables

Domaines: Algèbres d'opérateurs [math.OA]

Yoann Dabrowski. A Free Stochastic Partial Differential Equation. Annales de l'Institut Henri Poincaré, 2014, 50 (4), pp.1404-1455. ⟨10.1214/13-AIHP548⟩. ⟨hal-00948993⟩