Extending the Parisi formula along a Hamilton-Jacobi equation
Probability
2020-09-30 v2
Abstract
We study the free energy of mixed -spin spin glass models enriched with an additional magnetic field given by the canonical Gaussian field associated with a Ruelle probability cascade. We prove that this free energy converges to the Hopf-Lax solution of a certain Hamilton-Jacobi equation. Using this result, we give a new representation of the free energy of mixed -spin models with soft spins.
Keywords
Cite
@article{arxiv.1910.14482,
title = {Extending the Parisi formula along a Hamilton-Jacobi equation},
author = {Jean-Christophe Mourrat and Dmitry Panchenko},
journal= {arXiv preprint arXiv:1910.14482},
year = {2020}
}
Comments
16 pages