论文标题
几何随机图上的$ k $ cap过程
The $k$-Cap Process on Geometric Random Graphs
论文作者
论文摘要
图表上的$ k $ -cap（或$ k $ -winner-take-all）过程如下：在每次迭代中，恰好的$ k $顶点在上限（即获奖者）中；下一轮的获胜者是目前获胜者的总学位最高的顶点，并随机打破了联系。这种自然过程是大脑发射活动的简单模型。我们研究其在几何随机图上的收敛性，揭示了相当令人惊讶的行为。
The $k$-cap (or $k$-winners-take-all) process on a graph works as follows: in each iteration, exactly $k$ vertices of the graph are in the cap (i.e., winners); the next round winners are the vertices that have the highest total degree to the current winners, with ties broken randomly. This natural process is a simple model of firing activity in the brain. We study its convergence on geometric random graphs, revealing rather surprising behavior.
