Recurrence of the frog model on the 3,2-alternating tree
Recurrence of the frog model on the 3,2-alternating tree
复制标题
青蛙模型在3,2-交替树上的递归
DOI：
10.30757/alea.v15-30
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
J. Rosenberg
中科院分区：
文献类型：
--
作者：
J. Rosenberg
考虑一个在3，2-交替树上随机游动的增长系统，其中节点的世代在有两个和三个孩子之间交替。任何时候，一个粒子落在一个以前没有被访问过的节点上，一个新的粒子就会在这个节点上被激活，并开始它自己的随机行走。所描述的模型属于被统称为青蛙模型的一类问题。建立在最近的递归证明（这意味着无限多的青蛙击中根的概率为1）的正规二叉树，本文建立递归的3，2-交替的情况下。
Consider a growing system of random walks on the 3,2-alternating tree, where generations of nodes alternate between having two and three children. Any time a particle lands on a node which has not been visited previously, a new particle is activated at that node, and begins its own random walk. The model described belongs to a class of problems that are collectively referred to as the frog model. Building on a recent proof of recurrence (meaning infinitely many frogs hit the root with probability one) on the regular binary tree, this paper establishes recurrence for the 3,2-alternating case.