Gradient flow approach to local mean-field spin systems
Abstract
It is well-known that many diffusion equations can be recast as Wasserstein gradient flows. Moreover, in recent years, by modifying the Wasserstein distance appropriately, this technique has been transferred to further evolution equations and systems. In this paper we establish such a gradient flow representation for evolution equations that depend on a non-evolving parameter. These equations are connected to a local mean-field interacting spin system. We then use this gradient flow representation to prove a large deviation principle for the empirical process associated to this system. This is done by using a criterion that was established by Max Fathi in 2016. Finally, the corresponding hydrodynamic limit is shown by using an approach that was initiated by Sandier and Serfaty in 2004.
Cite
@article{arxiv.1806.07121,
title = {Gradient flow approach to local mean-field spin systems},
author = {Kaveh Bashiri and Anton Bovier},
journal= {arXiv preprint arXiv:1806.07121},
year = {2020}
}
Comments
In the newest version we corrected some minor typos and mistakes from the published version