Stationary Harmonic Measure and DLA in the Upper Half Plane
Stationary Harmonic Measure and DLA in the Upper Half Plane
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DOI：
10.1007/s10955-019-02327-y
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发表时间：
2017-11
影响因子：
1.6
通讯作者：
Eviatar B. Procaccia;Y. Zhang
中科院分区：
文献类型：
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作者：
Eviatar B. Procaccia;Y. Zhang
本文引入了上半平面上的平稳谐波测度。通过约束这一测度，我们可以在吸收边界条件下定义上半平面上的离散时间和连续时间扩散有限聚集（DLA）。我们证明了对于连续模型，增长率的上界为。此外，我们证明了所有的矩对于集合的大小都是有限的。当时间是离散的，我们还证明了n时刻骨料最大高度的一个较好的上界。本文发展的一个重要工具是界面生长过程，它约束任何根据平稳调和测度生长的过程。与[12]一起，我们可以得到任何这样的过程的非零增长率。
In this paper, we introduce the stationary harmonic measure in the upper half plane. By bounding this measure, we are able to define both the discrete and continuous time diffusion limited aggregation (DLA) in the upper half plane with absorbing boundary conditions. We prove that for the continuous model the growth rate is bounded from above by. Moreover we prove that all the moments are finite for the size of the aggregation. When time is discrete, we also prove a better upper bound of, on the maximum height of the aggregate at time n. An important tool developed in this paper, is an interface growth process, bounding any process growing according to the stationary harmonic measure. Together with [12] one obtains non zero growth rate for any such process.