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

报 告 人：宋健 教授 山东尊龙凯时

报告时间：2020年6月22日 10：00-11：00

报告地点：腾讯会议ID：690 608742

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

校内联系人：韩月才 hanyc@mdjtykj.cn

报告摘要：

Weconsider a directed polymer model in dimension 1 + 1, where the disorder isgiven by the occupation field of a Poisson system of independent random walkson Z. In a suitable continuum and weak disorder limit, we show that the familyof quenched partition functions of the directed polymer converges to theStratonovich solution of a multiplicative stochastic heat equation (SHE) with aGaussian noise, whose space-time covariance is given by the heat kernel. Incontrast to the case with space-time white noise where the solution of the SHEadmits a Wiener-Ito chaos expansion, we establish an L1-convergent chaos expansionsof iterated integrals generated by Picard iterations. Using this expansion andits dis- crete counterpart for the polymer partition functions, the convergenceof the terms in the expansion is proved via functional analytic arguments andheat kernel estimates. The Poisson random walk system is amenable to carefulmoment analysis, which is an important input to our arguments. This is a jointwork with Hao Shen, Rongfeng Sun and Lihu Xu.

报告人简介：

宋健，山东尊龙凯时教授，2010年博士于美国堪萨斯尊龙凯时，先后于美国Rutgers尊龙凯时New Brunswick分校、香港尊龙凯时工作，2018年任山东尊龙凯时教授。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。