报告人：朱蓉禅（北京理工大学）

时间：2023年09月22日 15:00-

腾讯会议ID：688 334 985

摘要：In this talk, we talk about the large $N$ problems for the Wick renormalized linear sigma model, i.e. $N$-component $\Phi^4$ model, in two spatial dimensions, using stochastic quantization methods and Dyson--Schwinger equations. We identify the large $N$ limiting law of a collection of Wick renormalized $O(N)$ invariant observables. In particular, under a suitable scaling, the quadratic observables converge in the large $N$ limit to a mean-zero (singular) Gaussian field $\mathcal{Q}$ with an explicit covariance; and the observables which are renormalized powers of order $2n$ converge in the large $N$ limit to suitably renormalized $n$-th powers of $\mathcal{Q}$. Furthermore, we derive the $1/N$ expansion for the $k$-point functions of the quadratic observables by employing a graph representation and carefully analyzing the order of each graph from Dyson-Schwinger equations. Finally, we obtain the next order stationary dynamics.

简介：朱蓉禅，教授，博士生导师，国家高层次人才，国家优秀青年基金获得者。本科毕业于四川大学、博士由中科院数学与系统科学研究院与德国比勒菲尔德大学联合培养。德国比勒菲尔德大学访问学者。长期从事随机偏微分方程、狄氏型、随机分析的研究工作。 以第一/通讯作者在Communications on Pure and Applied Mathematics, The Annals of Probability, Probability Theory and Related Fields, Communication in Mathematical Physics, Journal of Functional Analysis等期刊发表SCI论文30余篇。

邀请人：周国立

欢迎广大师生积极参与！