论文标题
超出$ l^2 $ - 阶段的弱点中的分区功能的波动
Fluctuations of partition functions of directed polymers in weak disorder beyond the $L^2$-phase
论文作者
论文摘要
我们在弱点中研究了有界环境中的定向聚合物模型，但没有$ l^2 $结合的性质，尤其是字段$（w_n^{0，x}）_ {x \ in \ mathbb z^d} $的同质化速度，其中$ w_n^{$ w_n^{0，x} $ demotes $ demotes $ demotes the polymering $ the $ the $ the $ the $ x $我们表明，在一组直径$ n^{1/2} $收敛到零的直径$ n^{ - ξ+o（1）} $上，适当地重新定位了空间平均值，其中指数是反温度$β$的显式函数。
We study the directed polymer model in a bounded environment in weak disorder but without $L^2$-boundedness, specifically the speed of homogenization for the field $(W_n^{0,x})_{x\in\mathbb Z^d}$, where $W_n^{0,x}$ denotes the associated martingale for the polymer starting from $x$. We show that a suitably re-centered spatial average over a set of diameter $n^{1/2}$ convergence to zero at rate $n^{-ξ+o(1)}$, where the exponent is an explicit function of the inverse temperature $β$.
