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

Chen, Wei-Kuo

doi:10.1090/S0002-9939-2015-12399-4

Partial results on the convexity of the Parisi functional with PDE approach
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by Wei-Kuo Chen

Proc. Amer. Math. Soc. 143 (2015), 3135-3146

DOI: https://doi.org/10.1090/S0002-9939-2015-12399-4

Published electronically: March 13, 2015

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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.

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