| 拟顶点可迁图上简单随机游走的切割点 |
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| 引用本文： | 宋贺,向开南. 拟顶点可迁图上简单随机游走的切割点[J]. 数学学报, 2017, 60(6): 947-954 |
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| 作者姓名： | 宋贺 向开南 |
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| 作者单位： | 南开大学数学科学学院 天津 300071 |
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| 基金项目： | 国家自然科学基金资助项目（11271204，11671216） |
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| 摘 要： | 证明了体积增长不低于5次多项式的拟顶点可迁图上的简单随机游走几乎处处有无穷多个切割时,从而有无穷多个切割点.该结论在所论情形下肯定了Benjamini,Gurel-Gurevich和Schramm在文[2011,Cutpoints and resistance of random walk paths,Ann.Probab.,39(3):1122-1136]中提出的猜想:顶点可迁图上暂留简单随机游走几乎处处有无穷多个切割点.
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| 关 键 词： | 切割点 简单随机游走 暂留 拟顶点可迁图 |
Cutpoints for Simple Random Walks on Quasi-Transitive Graphs |
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| He SONG,Kai Nan XIANG. Cutpoints for Simple Random Walks on Quasi-Transitive Graphs[J]. Acta Mathematica Sinica, 2017, 60(6): 947-954 |
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| Authors: | He SONG Kai Nan XIANG |
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| Affiliation: | School of Mathematical Sciences, LPMC, Nankai University, Tianjin 300071, P. R. China |
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| Abstract: | We prove that a simple random walk on quasi-transitive graphs with the volume growth being at least as fast as a polynomial of degree 5 has a.s. infinitely many cut times, and hence infinitely many cutpoints. This confirms a conjecture raised by Benjamini, Gurel-Gurevich and Schramm[2011, Cutpoints and resistance of random walk paths, Ann. Probab., 39(3):1122-1136] that PATH of a simple random walk on any transient vertex-transitive graph has a.s. infinitely many cutpoints in the corresponding case. |
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| Keywords: | cutpoint simple random walk transience quasi-transitive graph |
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