论文标题
扩散：静止和扰动
Diffusion: Quiescence and Perturbation
论文作者
论文摘要
Duffy等人最初提出的扩散是芯片射击的一种变体，其中从高浓度到低浓度的地方流出的芯片。在变体的扰动扩散中，第一步涉及一个“扰动”，即即使扩散规则仅允许将芯片从富裕的顶点发送到较贫穷的顶点，一些顶点向其每个邻居发送芯片。扰动扩散使我们能够通过提出新的问题来扩展对扩散的研究，例如``给定初始配置，在受扰动后的顶点将在某些步骤中返回初始配置。我们在本文中给出了一些结果，例如，在每种情况下，我们在本文中均可在每个角度上遇到的特定范围的某些情况。路径尤其具有更具体的结果。
Originally proposed by Duffy et al., Diffusion is a variant of chip-firing in which chips from flow from places of high concentration to places of low concentration. In the variant, Perturbation Diffusion, the first step involves a "perturbation" in which some number of vertices send chips to each of their respective neighbours even though the rules of Diffusion only permit for chips to be sent from richer vertices to poorer vertices. Perturbation Diffusion allows us to expand our study of Diffusion by asking new questions such as ``Given an initial configuration, which vertices, when perturbed, will return the initial configuration after some number of steps in Diffusion." We give some results in this paper that begin to answer this question in the specific case of every vertex initially having 0 chips. We characterize some of the ways a graph can reach such a state in Perturbation Diffusion before focusing on paths in particular with more specific results.
