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

Wei-Kuo Chen

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arXiv · 1308.6559

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

Wei-Kuo Chen

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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 the recent work of Panchenko [3], he 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 his original proof and presents more general results.

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Wei-Kuo Chen. 2013-11-11. Partial results on the convexity of the Parisi functional with PDE approach. https://arxiv.org/abs/1308.6559

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