返回概率指数至多为1/2的非Liouville群
Non-Liouville groups with return probability exponent at most 1/2
摘要：
我们构造了一个不具有Liouville性质的有限生成群$G$，使得随机游动的返回概率满足$p_{2n}(e,e) \gtrsim e^{-n^{1/2 + o(1)}}$ .最近的结果表明，$1/2$确实是最小的可能返回概率指数的非刘维群。我们的构造是基于树型Schreier图上的置换圈积和对这类图上逆轨道的大偏差的分析。
英文摘要：
We construct a finitely generated group $G$ without the Liouville property such that the return probability of a random walk satisfies $p_{2n}(e,e) \gtrsim e^{-n^{1/2 + o(1)}}$. Recent results suggest that $1/2$ is indeed the smallest possible return probability exponent for non-Liouville groups. Our construction is based on permutational wreath products over tree-like Schreier graphs and the analysis of large deviations of inverted orbits on such graphs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
