A Dynamic Programming Approach to the Parisi Functional

Aukosh Jagannath; Ian Tobasco

doi:10.1090/proc/12968

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arXiv · 1502.04398

A Dynamic Programming Approach to the Parisi Functional

Aukosh Jagannath·Ian Tobasco

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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].

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BibTeX RIS

Aukosh Jagannath, Ian Tobasco. 2015-02-16. A Dynamic Programming Approach to the Parisi Functional. https://doi.org/10.1090/proc/12968

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