%0 Journal Article
%T Partial results on the convexity of the Parisi functional with PDE approach
%A Wei-Kuo Chen
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1308.6559v2