English Version





Scaling limit of a directed polymer among a Poisson field of independent walks

主 讲 人 :宋健    教授


地      点 :Tencent会议 972 983 697


In this talk,we consider a directedpolymer model in dimension 1+1, where the disorder is given by the occupationfield of a Poisson system of independent random walks on Z. In a suitable continuum and weak disorder limit, weshow that the family of quenched partition functions of the directed polymerconverges to the Stratonovich solution of a multiplicative stochastic heatequation (SHE) with a Gaussian noise, whose space-time covariance is given bythe heat kernel. In contrast to the case with space-time white noise where thesolution of the SHE admits a Wiener-It? chaos expansion, we establish anL1-convergent chaos expansions of iterated integrals generated by Picarditerations. Using this expansion and its discrete counterpart for the polymerpartition functions, the convergence of the terms in the expansion is provedvia functional analytic arguments and heat kernel estimates. The Poisson randomwalk system is amenable to careful moment analysis, which is an important inputto our arguments.


宋健,山东大学数学院教授,2010年博士毕业于美国堪萨斯大学,2010.9-2012.12月在美国Rutgers大学New Brunswick分校担任助理教授,2013.1-2018.8在香港大学担任助理教授。主要研究领域为随机偏微分方程、分数布朗运动、随机矩阵、随机分析及其应用(包括数理金融、信息论等)。相关研究成果发表在Annals of  Probability,Annals of AppliedProbability, Bernoulli, Annales de l'Institut Henri Poincaré Probabilités et Statistiques, Electronic Journal of Probability, SIAM Journal on MathematicalAnalysis,以及Stochastic Processes and Their Applications等概率论顶级期刊;受邀为Annals of  Probability, Stochastic Processes andTheir Applications 以及 Annales de l'InstitutHenri Poincaré Probabilités et Statistiques等著名数学杂志担任评审,为美国 NSA Mathematical Sciences Grant Program担任评审。

发布时间:2021-06-03 19:55:50

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