大规模增长模型的快速模拟
Fast simulation of large-scale growth models
摘要：
我们给出了一种算法，可以计算某些增长模型的最终状态，而无需计算所有中间状态。我们的技术是基于“最小作用原理”，其特征在于里程表功能的增长过程。从一个近似的里程表，我们相继纠正下和高估，并证明到达正确的最终状态。内部扩散限制聚集（IDLA）是适合我们的技术模型之一。IDLA中的边界涨落最近被证明是最多对数的增长集群的大小，但在对数前面的常数仍然是未知的。作为我们的方法的一个应用，我们计算的波动的大小超过两个数量级超出以前的模拟，并使用结果来估计这个常数。
英文摘要：
We give an algorithm that computes the final state of certain growth models without computing all intermediate states. Our technique is based on a "least action principle" which characterizes the odometer function of the growth process. Starting from an approximation for the odometer, we successively correct under- and overestimates and provably arrive at the correct final state. Internal diffusion-limited aggregation (IDLA) is one of the models amenable to our technique. The boundary fluctuations in IDLA were recently proved to be at most logarithmic in the size of the growth cluster, but the constant in front of the logarithm is still not known. As an application of our method, we calculate the size of fluctuations over two orders of magnitude beyond previous simulations, and use the results to estimate this constant.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
