Parisi's formula is a Hamilton-Jacobi equation in Wasserstein space
Probability
2019-07-03 v2 Disordered Systems and Neural Networks
Abstract
Parisi's formula is a self-contained description of the infinite-volume limit of the free energy of mean-field spin glass models. We show that this quantity can be recast as the solution of a Hamilton-Jacobi equation in the Wasserstein space of probability measures on the positive half-line.
Keywords
Cite
@article{arxiv.1906.08471,
title = {Parisi's formula is a Hamilton-Jacobi equation in Wasserstein space},
author = {Jean-Christophe Mourrat},
journal= {arXiv preprint arXiv:1906.08471},
year = {2019}
}
Comments
19 pages