Exponential decay or correlation for the stochastic process associated to the entropy penalized method (Q2390109)

Let \(T^n\) be the \(n\)-dimensional torus. The authors consider the Lagrangian \(L(x,v)\: T^n\times \mathbb{R}^N\to \mathbb{R}\) of the form \[ L(x,v) = \frac12| v| ^2 - U(x) + \{ P,v\}, \] where \(U\in C^1(T^n)\) and \(P\in \mathbb{R}^n\) is constant. The paper deals with the discrete time Aubry--Mather problem and the entropy penalized Mather method which provides a way to obtain approximations by continuous densities of the Aubry--Mather measure.