论文标题
固定随机沙珀模型在线上的均匀阈值
Uniform threshold for fixation of the stochastic sandpile model on the line
论文作者
论文摘要
我们考虑阿贝尔随机沙珀模型。在此模型中，当一个位点包含多个粒子时，将其视为不稳定。每个不稳定的站点都以$ 1 $的价格推翻，将其两个粒子发送到独立选择的相邻站点。我们表明，当初始平均密度小于$ 1/2 $时，该系统几乎可以肯定地固定。我们通过分析每个位点的总数的均衡次数是由大量粒子在砂粒动力学下访问的。
We consider the abelian stochastic sandpile model. In this model, a site is deemed unstable when it contains more than one particle. Each unstable site, independently, is toppled at rate $1$, sending two of its particles to neighbouring sites chosen independently. We show that when the initial average density is less than $1/2$, the system locally fixates almost surely. We achieve this bound by analysing the parity of the total number of times each site is visited by a large number of particles under the sandpile dynamics.
