论文标题
限制定理的一些长距离随机步行，在无扭转的nilpotent组上
Limit theorems for some long range random walks on torsion free nilpotent groups
论文作者
论文摘要
我们考虑自然的远程随机步行在无扭转的nilpotent群体上，并为这些步行而开发限制定理。给定最初的离散组$γ$和随机步行$（s_n）_ {n \ ge1} $由某种类型的对称概率度量$μ$驱动，我们构建了一个同质的nilpotent lie lie $ g_ \ bulet $ g_ \ bullet（γ，μ），这些$（γ，μ）带有一个适用于稳定的膨胀结构和稳定的稳定过程$（稳定的过程$）$（x_______________________t） Donsker型功能限制定理是随机步行的重新缩放版本的极限。该组的限制组和限制过程都取决于度量$μ$。另外，功能极限定理与局部限制定理相辅相成。
We consider a natural class of long range random walks on torsion free nilpotent groups and develop limit theorems for these walks. Given the original discrete group $Γ$ and a random walk $(S_n)_ {n\ge1}$ driven by a certain type of symmetric probability measure $μ$, we construct a homogeneous nilpotent Lie group $G_\bullet(Γ,μ)$ which carries an adapted dilation structure and a stable-like process $(X_t)_{ t\ge0}$ which appears in a Donsker-type functional limit theorem as the limit of a rescaled version of the random walk. Both the limit group and the limit process on that group depend on the measure $μ$. In addition, the functional limit theorem is complemented by a local limit theorem.
