報告題目：Scaling limit of a directed polymer among a Poisson field of independent walks
報 告 人：宋健 教授 山東大學
報告時間：2020年6月22日 10：00-11：00
報告地點：騰訊會議ID：690 608 742
會議鍊接：https://meeting.tencent.com/s/jPH7TOUh223i
校内聯系人：韓月才 hanyc@jlu.edu.cn
報告摘要：
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.
報告人簡介：
宋健，山東大學教授，2010年博士于美國堪薩斯大學，先後于美國Rutgers大學New Brunswick分校、香港大學工作，2018年任山東大學教授。宋健教授的研究方向為随機偏微分方程、随機矩陣、分數布朗運動、随機分析及其應用（包括随機控制、信息論、數理金融）等。
