UNSOLVED PROBLEMS CONCERNING RANDOM WALKS ON TREES
UNSOLVED PROBLEMS CONCERNING RANDOM WALKS ON TREES
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有关树上随机游走的未解决问题
DOI：
10.1007/978-1-4612-1862-3_18
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
Y. Peres
中科院分区：
文献类型：
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作者：
R. Lyons;Robin Pemantle;Y. Peres
我们陈述了一些未解决的问题，并描述了有关在树上随机行走的相关示例。大多数问题涉及随机步行的行为随漂移的行为：这些随机步行已在蒙特卡洛算法中用于从树的顶点进行采样。通常，它们的行为反映了基础树的大小和规律性。随机步行与电导有关。 Galton-Watson树电导的分布函数满足有趣的功能方程。这个分布函数是绝对连续的吗？
We state some unsolved problems and describe relevant examples concerning random walks on trees. Most of the problems involve the behavior of random walks with drift: e.g., is the speed on Galton-Watson trees monotonic in the drift parameter? These random walks have been used in Monte-Carlo algorithms for sampling from the vertices of a tree; in general, their behavior reflects the size and regularity of the underlying tree. Random walks are related to conductance. The distribution function for the conductance of Galton-Watson trees satisfies an interesting functional equation; is this distribution function absolutely continuous?