论文标题
二维花圈产品漂移的大量定律
Law of large numbers for the drift of two-dimensional wreath product
论文作者
论文摘要
我们证明了在二维板岩组上随机步行的漂移的大量定律，假设随机步行具有有限的$（2+ε）$ - 力矩。该结果与阿贝尔群体的经典示例形成鲜明对比，在$ n $ sptep之后的位移（按平均值进行标准化）不集中，并且限制了归一化$ n $ n $ step的位移的限制分布承认其支持的密度为$ [0，\ infty）$。我们研究了群体的进一步示例，其中一些具有随机步行，满足LLN的漂移和其他浓度现象不存在的示例，并研究该特性与组的渐近几何形状的关系。
We prove the law of large numbers for the drift of random walks on the two-dimensional lamplighter group, under the assumption that the random walk has finite $(2+ε)$-moment. This result is in contrast with classical examples of abelian groups, where the displacement after $n$ steps, normalised by its mean, does not concentrate, and the limiting distribution of the normalised $n$-step displacement admits a density whose support is $[0,\infty)$. We study further examples of groups, some with random walks satisfying LLN for drift and other examples where such concentration phenomenon does not hold, and study relation of this property with asymptotic geometry of groups.
