论文标题
扩展源内部DLA波动的缩放限制
Scaling Limits of Fluctuations of Extended-Source Internal DLA
论文作者
论文摘要
在先前的工作中，我们证明了莱文和佩雷斯的2D扩展源内部DLA（IDLA）为$δ^{3/5} $ - 如果$δ$是晶格大小，则接近其缩放限制。在本文中，我们研究了波动本身的缩放限制。也就是说，我们表明两个自然定义的误差函数，它们一次和始终一次测量晶格点的“迟到”，分别收敛到几何依赖性的高斯随机场。我们使用这些结果来计算与流动波动相关的点相关函数。在此过程中，我们在相关的Levine和Peres的可分开的沙珀模型的波动上展示了相似的$δ^{3/5} $。
In a previous work, we showed that the 2D, extended-source internal DLA (IDLA) of Levine and Peres is $δ^{3/5}$-close to its scaling limit, if $δ$ is the lattice size. In this paper, we investigate the scaling limits of the fluctuations themselves. Namely, we show that two naturally defined error functions, which measure the "lateness" of lattice points at one time and at all times, respectively, converge to geometry-dependent Gaussian random fields. We use these results to calculate point-correlation functions associated with the fluctuations of the flow. Along the way, we demonstrate similar $δ^{3/5}$ bounds on the fluctuations of the related divisible sandpile model of Levine and Peres.
