Random walks under slowly varying moment conditions on groups of polynomial volume growth
Random walks under slowly varying moment conditions on groups of polynomial volume growth
复制标题
在多项式体积增长组上缓慢变化矩条件下的随机游走
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Tianyi Zheng
中科院分区：
文献类型：
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作者：
L. Saloff‐Coste;Tianyi Zheng
令 $G$ 为有限生成的多项式体积增长群，配备字长 $|cdot|$。本文的目标是开发技术来研究由对称度量 $mu$ 驱动的随机游走的行为，使得对于任何 $epsilon>0$，$sum|cdot|^epsilonmu=infty$。特别是，在 $mu$ 具有有限弱对数矩的情况下，我们为返回概率提供了一个急剧的下界。
Let $G$ be a finitely generated group of polynomial volume growth equipped with a word-length $|cdot|$. The goal of this paper is to develop techniques to study the behavior of random walks driven by symmetric measures $mu$ such that, for any $epsilon>0$, $sum|cdot|^epsilonmu=infty$. In particular, we provide a sharp lower bound for the return probability in the case when $mu$ has a finite weak-logarithmic moment.