Correction: Random walk in a random environment and first-passage percolation on trees
Correction: Random walk in a random environment and first-passage percolation on trees
复制标题
修正：随机环境中的随机游走和树上的首次渗透
DOI：
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
Robin Pemantle
中科院分区：
文献类型：
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作者：
R. Lyons;Robin Pemantle
我们表明，在某些随机环境中的任意无限的局部有限树上的随机游动的瞬时性或复发性是由树的分支数，这是一个衡量的平均分支数每个顶点。这概括和统一了作者以前的工作。它还表明，相变点的边缘加强随机游动同样是由树的分支数。最后，我们证明了分支数决定了树上的第一次通过渗透率，也称为第一次出生问题。我们的技术依赖于准伯努利渗流和大偏差的结果。§
We show that the transience or recurrence of a random walk in certain random environments on an arbitrary infinite locally finite tree is determined by the branching number of the tree, which is a measure of the average number of branches per vertex. This generalizes and unifies previous work of the authors. It also shows that the point of phase transition for edge-reinforced random walk is likewise determined by the branching number of the tree. Finally, we show that the branching number determines the rate of first-passage percolation on trees, also known as the first-birth problem. Our techniques depend on quasi-Bernoulli percolation and large deviation results. §