A Free Stochastic Partial Differential Equation

Abstract

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^ω embeddability. This includes an N-tuple of q-Gaussian random variables e.g. for |q|N\leq 0.13.

57 pages, final published version, slightly weaker results with improved exposition

References in corpus (5)

• Non injectivity of the q-deformed von Neumann algebra
• Factoriality of Bozejko-Speicher von Neumann algebras
• A Note about proving non-$\Gamma$ under a finite non-microstates free Fisher information Assumption
• Gaussian Random Matrix Models for q-deformed Gaussian Random Variables
• A Note on Cyclic Gradients

Cited by in corpus (2)

• Absence of algebraic relations and of zero divisors under the assumption of full non-microstates free entropy dimension
• Absence of algebraic relations and of zero divisors under the assumption of finite non-microstates free Fisher information