Site recurrence for coalescing random walk
Site recurrence for coalescing random walk
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DOI：
10.1214/16-ecp5
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发表时间：
2015-10
期刊：
影响因子：
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通讯作者：
I. Benjamini;E. Foxall;O. Gurel-Gurevich;M. Junge;H. Kesten
中科院分区：
文献类型：
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作者：
I. Benjamini;E. Foxall;O. Gurel-Gurevich;M. Junge;H. Kesten
从图的每个顶点开始开始连续时间随机游走，并使粒子在碰撞时合并。我们使用一个对偶关系的选民模型，证明该过程是网站经常在有界度图，和高尔顿-沃森树的后代分布具有指数尾。我们证明了一个网站的占用概率的界限，以及一般的0-1法律。类似的结论也适用于粒子不返回的树上的聚结过程。
Begin continuous time random walks from every vertex of a graph and have particles coalesce when they collide. We use a duality relation with the voter model to prove the process is site recurrent on bounded degree graphs, and for Galton-Watson trees whose offspring distribution has exponential tail. We prove bounds on the occupation probability of a site, as well as a general 0-1 law. Similar conclusions hold for a coalescing process on trees where particles do not backtrack.