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Partial results on the convexity of the Parisi functional with PDE approach


Author: Wei-Kuo Chen
Journal: Proc. Amer. Math. Soc. 143 (2015), 3135-3146
MSC (2010): Primary 60K35, 82B44; Secondary 49K20, 39B62
DOI: https://doi.org/10.1090/S0002-9939-2015-12399-4
Published electronically: March 13, 2015
MathSciNet review: 3336637
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Abstract: We investigate the convexity problem for the Parisi functional defined on the space of the so-called functional ordered parameters in the Sherrington-Kirkpatrick model. In a recent work of Panchenko, it was proved that this functional is convex along one-sided directions with a probabilistic method. In this paper, we will study this problem with a PDE approach that simplifies the original proof and presents more general results.


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

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Additional Information

Wei-Kuo Chen
Affiliation: Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
Email: wkchen@math.uchicago.edu

DOI: https://doi.org/10.1090/S0002-9939-2015-12399-4
Keywords: Parisi formula, Sherrington-Kirkpatrick model
Received by editor(s): August 30, 2013
Received by editor(s) in revised form: October 25, 2013
Published electronically: March 13, 2015
Communicated by: Joachim Krieger
Article copyright: © Copyright 2015 American Mathematical Society

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