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.References
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Additional Information
- Aukosh Jagannath
- Affiliation: Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012
- MR Author ID: 989445
- Email: aukosh@cims.nyu.edu
- Ian Tobasco
- Affiliation: Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012
- MR Author ID: 1057469
- Email: tobasco@cims.nyu.edu
- Received by editor(s): September 1, 2015
- Received by editor(s) in revised form: September 18, 2015, and September 21, 2015
- Published electronically: December 22, 2015
- Communicated by: Mark M. Meerschaert
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 3135-3150
- MSC (2010): Primary 60K35, 82B44, 82D30, 49N90; Secondary 35Q82, 35K58, 49S05
- DOI: https://doi.org/10.1090/proc/12968
- MathSciNet review: 3487243