Parisi泛函的动态规划方法
A Dynamic Programming Approach to the Parisi Functional
摘要：
G.Parisi预言了一类平均场自旋玻璃强自由能热力学极限的一个重要变分公式。本文给出了利用随机动态规划和半线性偏微分方程研究Parisi泛函的一种基本方法。我们给出了一个推导的重要性质的Parisi偏微分方程避免使用Ruelle概率级联和Cole-Hopf变换。作为应用，我们给出了最近由Auffinger和Chen在[2]中证明的Parisi泛函的严格凸性的一个简单证明.
英文摘要：
G.Parisi predicted an important variational formula for the thermodynamic limit of the intensive free energy for a class of mean field spin glasses. In this paper, we present an elementary approach to the study of the Parisi functional using stochastic dynamic programing and semi-linear PDE. We give a derivation of important properties of the Parisi PDE avoiding the use of Ruelle Probability Cascades and Cole-Hopf transformations. As an application, we give a simple proof of the strict convexity of the Parisi functional, which was recently proved by Auffinger and Chen in [2].
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