Can I read $\Gamma$-convergence for a class of action functionals induced by gradients of convex functions on EtoBox?

$\Gamma$-convergence for a class of action functionals induced by gradients of convex functions by Ambrosio, Luigi; Baradat, Aymeric; Brenier, Yann is a scholarly article available to read on EtoBox.

What is $\Gamma$-convergence for a class of action functionals induced by gradients of convex functions about?

Given a real function $f$, the rate function for the large deviations of the diffusion process of drift $\nabla f$ given by the Freidlin-Wentzell theorem coincides with the time integral of the energy dissipation for the gradient flow associated with $f$. This paper is concerned with the stability in the hilbertian framework of this common action functional when $f$ varies. More precisely, we show that if $(f_h)_h$ is uniformly $\lambda$-convex for some $\lambda \in \mathbb{R}$ and converges towards $f$ in the sense of Mosco convergence, then the related functionals $\Gamma$-converge in the strong topology of curves.

Author

Ambrosio, Luigi; Baradat, Aymeric; Brenier, Yann

Published

2021

Language

EN