Partial results on the convexity of the parisi functional with pde approach

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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.

Original languageEnglish (US)
Pages (from-to)3135-3146
Number of pages12
JournalProceedings of the American Mathematical Society
Volume143
Issue number7
DOIs
StatePublished - 2015

Keywords

  • Parisi formula
  • Sherrington-kirkpatrick model

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