随机图与图极限上芯片燃烧的魔鬼阶梯
The devil's staircase for chip-firing on random graphs and on graphons
AI总结：
该研究将并行芯片燃烧推广到graphon，证明了Erdős–Rényi随机图上其活跃度图随顶点数增加收敛为魔鬼阶梯，还明确了graphon上活跃度的存在性条件。
摘要：
我们研究了Erdős–Rényi随机图上，随着芯片数量增加，并行芯片燃烧的活跃度表现。研究表明，在多种情形下，随着顶点数量增加，所得的活跃度图会收敛为魔鬼阶梯。我们的方法是将并行芯片燃烧推广到graphon（图极限），并证明活跃度的连续性结果。我们还发现，graphon上某一芯片配置的活跃度不一定存在，但对于一大类graphon上的所有芯片配置，活跃度均存在。
英文摘要：
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.
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。
