论文标题
关于青蛙在Galton-Watson树上的瞬变
On transience of frogs on Galton-Watson trees
论文作者
论文摘要
我们在无限的Galton-Watson树上考虑一个随机相互作用的粒子系统，称为青蛙模型，使后代为零，一个。该系统从树根上的一个清醒粒子（青蛙）开始，另一个顶点则是随机数量的睡眠颗粒。醒来的青蛙根据简单的随机步行在树上移动，一旦遇到睡眠青蛙，它们就会醒来并根据简单的随机步行独立移动。青蛙模型称为瞬态，如果几乎只有有限的许多粒子返回根部。在本文中，我们证明了青蛙模型的瞬时法则，并显示了某些类别的Galton-Watson树的瞬时阶段。
We consider a random interacting particle system, known as the frog model, on infinite Galton-Watson trees allowing offspring zero and one. The system starts with one awake particle (frog) at the root of the tree and a random number of sleeping particles at the other vertices. Awake frogs move according to simple random walk on the tree and as soon as they encounter sleeping frogs, those will wake up and move independently according to simple random walk. The frog model is called transient, if there are almost surely only finitely many particles returning to the root. In this paper we prove a zero-one law for transience of the frog model and show the existence of a transient phase for certain classes of Galton-Watson trees.
