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Article Dans Une Revue Rendiconti Lincei. Matematica e Applicazioni Année : 2021

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

Luigi Ambrosio
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Aymeric Baradat
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Résumé

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.
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Dates et versions

hal-03114814 , version 1 (19-01-2021)

Identifiants

Citer

Luigi Ambrosio, Aymeric Baradat, Yann Brenier. $\Gamma$-convergence for a class of action functionals induced by gradients of convex functions. Rendiconti Lincei. Matematica e Applicazioni, 2021, 3 (1), pp.97-108. ⟨10.4171/RLM/928⟩. ⟨hal-03114814⟩
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