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.
 

个人简介: 让光林，武汉大学数学与统计学院副教授、硕士生导师。主要从事随机分析、量子场理论等方面的研究工作，主持多项国家级和省部级科研项目，发表10多篇研究论文。