论文标题
固定的Hastings-Levitov的增长
Growth of Stationary Hastings-Levitov
论文作者
论文摘要
我们构建和研究Hastings-Levitov $（0）$型号的固定版本。我们证明，与经典的HL $（0）$模型不同，在固定案例中，附着在骨料上的粒子的大小很紧，因此提出了SHL $（0）$作为潜在的固定非晶格变体的潜在候选，用于扩散限制聚合（DLA）。固定设置以及对谐波度量的几何解释，产生了新的几何结果，例如稳定，手臂的有限和手臂尺寸分布。我们表明，在适当的缩放下，shl $（0）$中的武器收敛到布朗运动的图表，该图具有分形尺寸$ 3/2 $。此外，我们表明，具有$ n $颗粒的树木达到$ n^{2/3} $的订单高度，对应于1983年从1983年开始在长线段上生长的DLA的循环半径。
We construct and study a stationary version of the Hastings-Levitov$(0)$ model. We prove that, unlike in the classical HL$(0)$ model, in the stationary case the size of particles attaching to the aggregate is tight, and therefore SHL$(0)$ is proposed as a potential candidate for a stationary off-lattice variant of Diffusion Limited Aggregation (DLA). The stationary setting, together with a geometric interpretation of the harmonic measure, yields new geometric results such as stabilization, finiteness of arms and arm size distribution. We show that, under appropriate scaling, arms in SHL$(0)$ converge to the graph of Brownian motion which has fractal dimension $3/2$. Moreover we show that trees with $n$ particles reach a height of order $n^{2/3}$, corresponding to a numerical prediction of Meakin from 1983 for the gyration radius of DLA growing on a long line segment.
