A dynamic programming approach to the Parisi functional

Jagannath, Aukosh; Tobasco, Ian

doi:10.1090/proc/12968

A dynamic programming approach to the Parisi functional
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by Aukosh Jagannath and Ian Tobasco PDF

Proc. Amer. Math. Soc. 144 (2016), 3135-3150 Request permission

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.

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