论文标题
迭代对数的法律在灯塔对角线产品上
A Law of Iterated Logarithm on Lamplighter Diagonal Products
论文作者
论文摘要
我们证明了迭代的对数定律，用于在Brieussel和Zheng（2021）建造的对角线产品上随机步行。这为迭代对数行为的定律提供了各种各样的新示例，用于在小组上随机行走。特别是，因此，对于任何$ \ frac {1} {2} {2} \ leqβ\ leq 1 $，有一个$ g $和随机步行$ w_n $ on $ g $上的$ \ mathbb {e} | \ frac {| w_n |} {n^β（\ log \ log \ log n）^{1-β}} <\ infty $$和$$ 0 <\ liminf \ frac {| w_n |（\ log log \ log \ log \ log \ log \ log n）
We prove a Law of Iterated Logarithm for random walks on a family of diagonal products constructed by Brieussel and Zheng (2021). This provides a wide variety of new examples of Law of Iterated Logarithm behaviours for random walks on groups. In particular, it follows that for any $\frac{1}{2}\leq β\leq 1$ there is a group $G$ and random walk $W_n$ on $G$ with $\mathbb{E}|W_n|\simeq n^β$ such that $$0<\limsup \frac{|W_n|}{n^β(\log\log n)^{1-β}}<\infty$$ and $$0<\liminf \frac{|W_n|(\log\log n)^{1-β}}{n^β}<\infty.$$
