Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Partial results on the convexity of the Parisi functional with PDE approach
HTML articles powered by AMS MathViewer

by Wei-Kuo Chen PDF
Proc. Amer. Math. Soc. 143 (2015), 3135-3146 Request permission

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
Similar Articles
Additional Information
  • Wei-Kuo Chen
  • Affiliation: Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
  • MR Author ID: 1008839
  • Email: wkchen@math.uchicago.edu
  • 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: https://doi.org/10.1090/S0002-9939-2015-12399-4
  • MathSciNet review: 3336637