The Parisi Formula via Stochastic Analysis
Prof. Elton P. HsuNorthwestern University 10:30 – 12:00 鴻經館 M107
Abstract：
The Parisi formula is a fundamental result in spin glass theory. In this talk I will present a new approach to (an enhanced Version of) Guerra's identity, from which the upper bound in the Parisi formula follows immediately. Among the techniques from stochastic analysis we will use include path space integration parts for the Wiener measure (Brownian motion), the Girsanov transform (exponential martingales), and the Feynman-Kac formula. The key observation is that the nonlinear partial differentiation equation figuring in Parisi’s variation formula becomes linear after differentiating with respect to a parameter, thus allowing the full strength of stochastic analysis based on Ito’s calculus into play. We hope that this approach will shed some lights on the much more difficult lower bound in the Parisi formula.
20230615演講_Prof. Elton P. Hsu (Northwestern University)