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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Partial results on the convexity of the Parisi functional with PDE approach
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by Wei-Kuo Chen PDF
Proc. Amer. Math. Soc. 143 (2015), 3135-3146 Request permission


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.
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Additional Information
  • Wei-Kuo Chen
  • Affiliation: Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
  • MR Author ID: 1008839
  • Email:
  • 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
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 3135-3146
  • MSC (2010): Primary 60K35, 82B44; Secondary 49K20, 39B62
  • DOI:
  • MathSciNet review: 3336637