Fluctuation-dissipation relations for reversible diffusions

This lecture by Pierre Mathieu in January 2021 discusses linear response and steady states for reversible diffusions in a random environment. It covers the symmetric diffusion process, effective drift, perturbed dynamics, Girsanov transforms, and the structure of the response term. The lecture explores the covariance matrix, scaling limits, and applications to linear response, emphasizing the Nyquist relations and the Central Limit Theorem. It also delves into the existence of steady states, thermalization time, and the H-1(Q) space for observables. The presentation concludes with discussions on covariance limits, Gaussian laws, and weak forms of linear response.