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        From Directed Polymers in Spatial-correlated Environment to Stochastic Heat Equations Driven by Fractional Noise in $1+1$ Dimensions, 讓光林, L2620, 2018.6.2, 下午2:45
        2018-06-06 09:57  

        Abstract:  In this talk we consider the limit behavior of partition function of directed polymers in random environment represented by linear model instead of a family of i.i.d.variables in $1+1$ dimensions. Under the assumption that the correlation decays algebraically, using the method developed in [Ann. Probab., 42(3):1212-1256, 2014], under a new scaling we show the scaled partition function as a process defined on $[0,1]\times\RR$, converges weakly to the solution to some stochastic heat equations driven by fractional Brownian field. The Hurst parameter is determined by the correlation exponent of the random environment. Here multiple It\^{o} integral with respect to fractional Gaussian field and spectral representation of stationary process are heavily involved.


        個人簡介: 讓光林,武漢大學數學與統計學院副教授、碩士生導師。主要從事隨機分析、量子場理論等方面的研究工作,主持多項國家級和省部級科研項目,發表10多篇研究論文。

        Three Gorges Math Research Center  443002, Yichang, Hubei