A gradient flow approach to large deviations for diffusion processes

TL;DR

This paper explores the connection between gradient flow formulations of diffusion processes and large deviation principles, establishing an equivalence and applying it to models like Ginzburg-Landau with Kawasaki dynamics.

Contribution

It introduces a novel link between gradient flow approaches and large deviations, proving an equivalence via Gamma-convergence and applying it to complex particle systems.

Findings

Established equivalence between LDP and Gamma-convergence in gradient flow context

Analyzed large deviations from hydrodynamic limits in Ginzburg-Landau models

Provided a mathematical framework connecting probabilistic and variational approaches

Abstract

In this work, we investigate links between the formulation of the flow of marginals of reversible diffusion processes as gradient flows in the space of probability measures and path wise large deviation principles for sequences of such processes. An equivalence between the LDP principle and Gamma-convergence for a sequence of functionals appearing in the gradient flow formulation is proved. As an application, we study large deviations from the hydrodynamic limit for two variants of the Ginzburg-Landau model endowed with Kawasaki dynamics.