论文标题
DLA手臂生长的玩具模型
A toy model for DLA arm growth in a wedge
论文作者
论文摘要
在本文中，我们考虑了一个非均匀的离散时间马尔可夫链，该链可以被视为在亚线性楔形物中DLA（扩散限制聚集）过程生长的玩具模型。猜想是，在足够薄的线性楔形物中，DLA簇中只有一个无限臂，我们在模型中证明了这种现象。该技术遵循一个自举论点，在该论点中，我们迭代地证明了更快的增长率。
In this paper, we consider a non-homogeneous discrete-time Markov chain which can be seen as a toy model for the growth of the arms of the DLA (Diffusion limited aggregation) process in a sub-linear wedge. It is conjectured that in a thin enough linear wedge there is only one infinite arm in the DLA cluster and we demonstrate this phenomenon in our model. The technique follows a bootstrapping argument, in which we iteratively prove ever faster growth rate.
