Scaling limits for planar aggregation with subcritical fluctuations
Scaling limits for planar aggregation with subcritical fluctuations
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DOI：
10.1007/s00440-022-01141-0
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发表时间：
2019-02
影响因子：
2
通讯作者：
J. Norris;Vittoria Silvestri;Amanda G. Turner
中科院分区：
文献类型：
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作者：
J. Norris;Vittoria Silvestri;Amanda G. Turner
我们研究了一类平面随机生长过程的标度极限，在这个过程中，团簇是由小粒子的连续聚集而生长的。在这些模型中，簇被编码为共形映射的组合，每个连续粒子的位置根据簇边界上的调和测度的密度进行分布，并提高到一定的幂。我们表明，当这个权力位于一个特定的范围内，集群的宏观形状收敛到一个磁盘，但作为权力接近这个范围的边缘的波动接近临界点，这是一个极限的稳定性。在本文中开发的方法提供了一个蓝图，用于分析更一般的随机增长模型，如Hastings-Levitov家庭。
We study scaling limits of a family of planar random growth processes in which clusters grow by the successive aggregation of small particles. In these models, clusters are encoded as a composition of conformal maps and the location of each successive particle is distributed according to the density of harmonic measure on the cluster boundary, raised to some power. We show that, when this power lies within a particular range, the macroscopic shape of the cluster converges to a disk, but that as the power approaches the edge of this range the fluctuations approach a critical point, which is a limit of stability. The methodology developed in this paper provides a blueprint for analysing more general random growth models, such as the Hastings-Levitov family.