Hamilton-Jacobi equations for mean-field disordered systems
Probability
2018-11-13 v2 Disordered Systems and Neural Networks
Abstract
We argue that Hamilton-Jacobi equations provide a convenient and intuitive approach for studying the large-scale behavior of mean-field disordered systems. This point of view is illustrated on the problem of inference of a rank-one matrix. We compute the large-scale limit of the free energy by showing that it satisfies an approximate Hamilton-Jacobi equation with asymptotically vanishing viscosity parameter and error term.
Cite
@article{arxiv.1811.01432,
title = {Hamilton-Jacobi equations for mean-field disordered systems},
author = {Jean-Christophe Mourrat},
journal= {arXiv preprint arXiv:1811.01432},
year = {2018}
}
Comments
29 pages, v2: tensor case added