报告题目：Scaling Limit of a Directed Polymer Among a Poisson Field of Independent Walks

报告人：宋健 教授(山东大学数学与交叉科学研究中心)

报告时间：2020-12-22  10:00-11:00

腾讯会议ID：106 855 870

报告入口：https://meeting.tencent.com/s/TO17ExLIAiEI

Abstract: 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 discrete 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.