Diffusion-limited aggregation on a tree
Diffusion-limited aggregation on a tree
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树上的扩散限制聚合
DOI：
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发表时间：
1997
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影响因子：
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通讯作者：
E. Perkins
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文献类型：
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作者：
M. Barlow;Robin Pemantle;E. Perkins
摘要我们研究了正则d叉树上的增长模型。与现有子树相邻的距离为n的点以与α−n成比例的概率添加，其中α < 1是正的真实的参数。这些星系团的高度随着它们的总尺寸线性增加;这补充了已知的结果，即当α = 1时，高度只以几何方式增加。使用随机单调性和再生的结果，这可能是独立的利益。我们的动机来自其他两种方式，在该模型可以被视为：作为一个问题，在第一次通过渗流，并作为一个版本的扩散限制聚集（DLA），调整，使“指”发生。
Summary. We study the following growth model on a regular d-ary tree. Points at distance n adjacent to the existing subtree are added with probabilities proportional to α−n, where α < 1 is a positive real parameter. The heights of these clusters are shown to increase linearly with their total size; this complements known results that show the height increases only logarithmically when α≧ 1. Results are obtained using stochastic monotonicity and regeneration results which may be of independent interest. Our motivation comes from two other ways in which the model may be viewed: as a problem in first-passage percolation, and as a version of diffusion-limited aggregation (DLA), adjusted so that “fingering” occurs.