论文标题
魔鬼的楼梯，用于在随机图上和图形上进行芯片射击
The devil's staircase for chip-firing on random graphs and on graphons
论文作者
论文摘要
我们研究了在增加erdős-rényi随机图上增加芯片数量的平行芯片活动活性的行为。我们表明，在各种情况下，随着我们增加顶点的数量，所得的活动图会收敛到魔鬼的楼梯。我们的方法是将并行芯片概括为图形，并证明活动的连续性结果。我们还表明，芯片配置在图形子上的活动不一定存在，但是它确实存在于大型Graphons上的每个芯片配置。
We study the behavior of the activity of the parallel chip-firing upon increasing the number of chips on an Erdős--Rényi random graph. We show that in various situations the resulting activity diagrams converge to a devil's staircase as we increase the number of vertices. Our method is to generalize the parallel chip-firing to graphons, and to prove a continuity result for the activity. We also show that the activity of a chip configuration on a graphon does not necessarily exist, but it does exist for every chip configuration on a large class of graphons.
