JournalsrlmVol. 32, No. 1pp. 97–108

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

  • Luigi Ambrosio

    Scuola Normale Superiore, Pisa, Italy
  • Aymeric Baradat

    Université Lyon 1, Villeurbanne, France
  • Yann Brenier

    École Normale Supérieure, Paris, France
$\Gamma$-convergence for a class of action functionals induced by gradients of convex functions cover
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Abstract

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

Cite this article

Luigi Ambrosio, Aymeric Baradat, Yann Brenier, Γ\Gamma-convergence for a class of action functionals induced by gradients of convex functions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 32 (2021), no. 1, pp. 97–108

DOI 10.4171/RLM/928