论文标题
Edwards-Wilkinson在整个$ l^2 $ - 尺寸中的定向聚合物的波动$ d \ geq 3 $
Edwards-Wilkinson fluctuations for the directed polymer in the full $L^2$-regime for dimensions $d \geq 3$
论文作者
论文摘要
我们证明，在整个$ l^2 $ - 权利中，在尺寸中，有向聚合物模型的分区函数$ d \ geq 3 $，如果居中，缩放和平均相对于测试功能$φ\ in C_C（\ Mathbb {r}^d）$中的c_c（\ mathbb {r}^d）$，将分配给gaussian随机变量。在这种情况下，在这种情况下引入了一个新想法，我们还证明，当对测试函数的居中和平均时，可以将日志分区函数视为KPZ方程的离散化表现出相同的波动。因此，这两个模型属于Edwards-Wilkinson普遍级别的整个$ l^2 $ - 政权，这是迄今为止仅在$ d \ geq 3 $中的严格子集中建立的结果。
We prove that in the full $L^2$-regime the partition function of the directed polymer model in dimensions $d\geq 3$, if centered, scaled and averaged with respect to a test function $φ\in C_c(\mathbb{R}^d)$, converges in distribution to a Gaussian random variable with explicit variance. Introducing a new idea in this context of a martingale difference representation, we also prove that the log-partition function, which can be viewed as a discretisation of the KPZ equation, exhibits the same fluctuations, when centered and averaged with respect to a test function. Thus, the two models fall within the Edwards-Wilkinson universality class in the full $L^2$-regime, a result that was only established, so far, for a strict subset of this regime in $d\geq 3$.
