A Dynamic Programming Approach to the Parisi Functional
Probability
2017-03-08 v4 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
G.Parisi predicted an important variational formula for the thermodynamic limit of the intensive free energy for a class of mean field spin glasses. In this paper, we present an elementary approach to the study of the Parisi functional using stochastic dynamic programing and semi-linear PDE. We give a derivation of important properties of the Parisi PDE avoiding the use of Ruelle Probability Cascades and Cole-Hopf transformations. As an application, we give a simple proof of the strict convexity of the Parisi functional, which was recently proved by Auffinger and Chen in [2].
Cite
@article{arxiv.1502.04398,
title = {A Dynamic Programming Approach to the Parisi Functional},
author = {Aukosh Jagannath and Ian Tobasco},
journal= {arXiv preprint arXiv:1502.04398},
year = {2017}
}
Comments
Edits to take in to account referee's comments and suggestions. To appear in Proceedings of the AMS