Stochastic quantization to perturbation theory of $\Phi^4_2$: asymptoticity and short distance
报告题目(Title)：Stochastic quantization to perturbation theory of $\Phi^4_2$: asymptoticity and short distance
报告人(Speaker)：朱蓉禅(北京理工大学)
地点(Place)：教八-210
时间(Time)：2021 年11 月1 日(周一) 下午3:40-4:40
邀请人(Inviter)：蒲飞
报告摘要
In this talk we study the perturbation theory of$\Phi^4_2$ model on the whole plane via stochastic quantization. We use integration by parts formula (i.e. Dyson-Schwinger equations) to generate the perturbative expansion for the $k$-point correlation functions, and prove bounds on the remainder of the truncated expansion using SPDE estimates; this in particular proves that the expansion is asymptotic. Furthermore, we derive short distance behaviors of the $2$-point function and the connected $4$-point function, also via suitable Dyson-Schwinger equations combined with SPDE arguments. This talk is based on joint work with Hao Shen and Xiangchan Zhu.
