# Exponential convergence to the stationary measure and hyperbolicity of the minimisers for random Lagrangian

## Main Article Content

## Abstract

We consider a class of 1d Lagrangian systems with random forcing in the space-periodic setting. These systems have been studied since the 1990s by Khanin, Sinai and their collaborators [7, 9, 11, 15].Here we give an overview of their results and then we expose our recent proof of the exponential convergence to the stationary measure [6]. This is the first such result in a classical setting, i.e. in the dual-Lipschitz metric with respect to the Lebesgue space $L_p$ for finite $p$, partially answering the conjecture formulated in \cite{GIKP05}. In the multidimensional setting, a more technically involved proof has been recently given by Iturriaga, Khanin ans Zhang [13].

## Article Details

How to Cite

Boritchev, A.
(2017).
Exponential convergence to the stationary measure and hyperbolicity of the minimisers for random Lagrangian.

*Proceedings Of Equadiff 2017 Conference,*, 117-126. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/equadiff/article/view/784/555
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Articles