Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

A dynamic programming approach to the Parisi functional


Authors: Aukosh Jagannath and Ian Tobasco
Journal: Proc. Amer. Math. Soc. 144 (2016), 3135-3150
MSC (2010): Primary 60K35, 82B44, 82D30, 49N90; Secondary 35Q82, 35K58, 49S05
Published electronically: December 22, 2015
MathSciNet review: 3487243
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 60K35, 82B44, 82D30, 49N90, 35Q82, 35K58, 49S05

Retrieve articles in all journals with MSC (2010): 60K35, 82B44, 82D30, 49N90, 35Q82, 35K58, 49S05


Additional Information

Aukosh Jagannath
Affiliation: Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012
Email: aukosh@cims.nyu.edu

Ian Tobasco
Affiliation: Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012
Email: tobasco@cims.nyu.edu

DOI: https://doi.org/10.1090/proc/12968
Keywords: Parisi formula, Sherrington-Kirkpatrick model, dynamic programming
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
Article copyright: © Copyright 2015 American Mathematical Society