Upper bounds on the growth rate of Diffusion Limited Aggregation
Upper bounds on the growth rate of Diffusion Limited Aggregation
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发表时间：
2017-05
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通讯作者：
I. Benjamini;Ariel Yadin
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作者：
I. Benjamini;Ariel Yadin
我们重温了凯斯滕关于DLA增长率上限的论点。我们能够使这一论点足够稳健，以至于它适用于许多只需要控制热核的图。我们将它应用于许多例子，包括多项式增长的传递图、指数增长图、不可服从图、Z^d上的超临界渗流、高维Pre-Sierpinski地毯。我们还观察到，仔细的分析表明，Kesten在Z^3上的原始界可以从t^{2/3}改进到(Tlogt)^{1/2}。
We revisit Kesten's argument for the upper bound on the growth rate of DLA. We are able to make the argument robust enough so that it applies to many graphs, where only control of the heat kernel is required. We apply this to many examples including transitive graphs of polynomial growth, graphs of exponential growth, non-amenable graphs, super-critical percolation on Z^d, high dimensional pre-Sierpinski carpets. We also observe that a careful analysis shows that Kesten's original bound on Z^3 can be improved from t^{2/3} to (t log t)^{1/2} .