含稀有事件的扩散限制集的调和测度
The Harmonic Measure of Diffusion-Limited Aggregates including Rare Events
摘要：
我们使用有偏随机游走采样技术获得了扩散限制聚集（DLA）集群的谐波测度，该技术使我们能够以前所未有的精度测量随机游走器击中集群部分的概率;我们的结果包括小至10^（-80）的概率。我们发现多重分形D（q）谱包括小q和负q的区域。我们的算法使我们能够获得集群的谐波测量大于一个数量级以上的使用迭代共形映射，这是以前最好的方法的方法实现。我们发现在奇异谱f（alpha）中在α近似等于14处有一个相变，并且还发现D（q）的最小q，q_{min} = 0.9 ± 0.05。
英文摘要：
We obtain the harmonic measure of diffusion-limited aggregate (DLA) clusters using a biased random-walk sampling technique which allows us to measure probabilities of random walkers hitting sections of clusters with unprecedented accuracy; our results include probabilities as small as 10^(-80). We find the multifractal D(q) spectrum including regions of small and negative q. Our algorithm allows us to obtain the harmonic measure for clusters more than an order of magnitude larger than those achieved using the method of iterative conformal maps, which is the previous best method. We find a phase transition in the singularity spectrum f(alpha) at alpha approximately equal to 14 and also find a minimum q of D(q), q_{min} = 0.9 plus or minus 0.05.
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