标题： 相对双曲群关于虚拟幂零子群的局部极限定理 显示英文标题

标题： Local limit theorems on relatively hyperbolic groups with respect to virtually nilpotent subgroups

摘要： 给定一个有限生成群上的概率测度，局部极限问题在于找到$p_n(e,e)$的渐进行为，即在时间$n$时随机游走位于原点的概率。 我们给出了相对于虚拟阿贝尔子群的相对双曲群上所有可能的局部极限定理的分类，最多存在有界误差，对于有限支集、对称且可接受的概率测度。 显示英文摘要

摘要： Given a probability measure on a finitely generated group, the local limit problem consists in finding asymptotics of $p_n(e,e)$, the probability that the random walk at time $n$ is at the origin. We give the classification of all possible local limit theorems, up to bounded error, for finitely supported, symmetric, admissible probability measures on a relatively hyperbolic group with respect to virtually nilpotent subgroups.