论文标题
平面中扩展源内部DLA的收敛速率
A Convergence Rate for Extended-Source Internal DLA in the Plane
论文作者
论文摘要
内部DLA（IDLA）是一种内部聚合模型，其中粒子依次从原点进行随机步行，并在到达未占用位点后停止。莱文（Levine）和佩雷斯（Peres）表明，当粒子从固定的多点分布开始时，修改后的IDLA过程具有与某些障碍问题有关的确定性缩放限制。在本文中，我们研究了平面中此“扩展源” IDLA的收敛速率，以达到其缩放限制。我们表明，如果$δ$是晶格的大小，则IDLA占用集的波动最多是$δ^{3/5} $从其缩放限制中的，概率至少为$ 1-e^{ - 1/δ^{2/2/5}}} $。
Internal DLA (IDLA) is an internal aggregation model in which particles perform random walks from the origin, in turn, and stop upon reaching an unoccupied site. Levine and Peres showed that, when particles start instead from fixed multiple-point distributions, the modified IDLA processes have deterministic scaling limits related to a certain obstacle problem. In this paper, we investigate the convergence rate of this "extended source" IDLA in the plane to its scaling limit. We show that, if $δ$ is the lattice size, fluctuations of the IDLA occupied set are at most of order $δ^{3/5}$ from its scaling limit, with probability at least $1-e^{-1/δ^{2/5}}$.
