# $\Gamma$-convergence for a class of action functionals induced by gradients of convex functions

@inproceedings{Ambrosio2021GammaconvergenceFA, title={\$\Gamma\$-convergence for a class of action functionals induced by gradients of convex functions}, author={Luigi Ambrosio and Aymeric Baradat and Yann Brenier}, year={2021} }

Given a real function f , the rate function for the large deviations of the diffusion process of drift ∇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 (fh)h is uniformly λ-convex for some λ ∈ R and converges towards f in the sense of Mosco convergence…

## One Citation

Stability of a class of action functionals depending on convex functions

- MathematicsDiscrete and Continuous Dynamical Systems
- 2022

<p style='text-indent:20px;'>We study the stability of a class of action functionals induced by gradients of convex functions with respect to Mosco convergence, under mild assumptions on the…

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