From transience to recurrence with Poisson tree frogs.
From transience to recurrence with Poisson tree frogs.
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泊松树蛙从短暂到复发。
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
M. Junge
中科院分区：
文献类型：
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作者：
C. Hoffman;Tobias Johnson;M. Junge
考虑以下d叉树上的相互作用粒子系统，称为青蛙模型：最初，一个粒子在根部醒来，i.i.d.泊松分布中，每隔一个顶点就有许多粒子处于休眠状态。清醒的粒子执行简单的随机行走，唤醒它们遇到的任何睡眠粒子。我们证明，有一个相变之间的瞬态和复发粒子的初始密度的增加，我们给的顺序过渡到一个对数因子。
Consider the following interacting particle system on the d-ary tree, known as the frog model: Initially, one particle is awake at the root and i.i.d. Poisson many particles are sleeping at every other vertex. Particles that are awake perform simple random walks, awakening any sleeping particles they encounter. We prove that there is a phase transition between transience and recurrence as the initial density of particles increases, and we give the order of the transition up to a logarithmic factor.