报告题目：Scaling limit of a directed polymer among a Poisson field of independent walks

报 告 人：宋健 教授 山东大学

报告时间：2020年6月22日 10：00-11：00

报告地点：腾讯会议ID：690 608 742

会议链接：https://meeting.tencent.com/s/jPH7TOUh223i

校内联系人：韩月才 hanyc@jlu.edu.cn

报告摘要：

We consider a directed polymer model in dimension 1 + 1, where the disorder is given by the occupation field of a Poisson system of independent random walks on Z. In a suitable continuum and weak disorder limit, we show that the family of quenched partition functions of the directed polymer converges to the Stratonovich solution of a multiplicative stochastic heat equation (SHE) with a Gaussian noise, whose space-time covariance is given by the heat kernel. In contrast to the case with space-time white noise where the solution of the SHE admits a Wiener-Ito chaos expansion, we establish an L1-convergent chaos expansions of iterated integrals generated by Picard iterations. Using this expansion and its dis- crete counterpart for the polymer partition functions, the convergence of the terms in the expansion is proved via functional analytic arguments and heat kernel estimates. The Poisson random walk system is amenable to careful moment analysis, which is an important input to our arguments. This is a joint work with Hao Shen, Rongfeng Sun and Lihu Xu.

报告人简介：

宋健，山东大学教授，2010年博士于美国堪萨斯大学，先后于美国Rutgers大学New Brunswick分校、香港大学工作，2018年任山东大学教授。宋健教授的研究方向为随机偏微分方程、随机矩阵、分数布朗运动、随机分析及其应用（包括随机控制、信息论、数理金融）等。