论文标题
相对双曲线组中的局部极限定理II：非光谱退化病例
Local limit theorems in relatively hyperbolic groups II : the non-spectrally degenerate case
论文作者
论文摘要
这是两篇论文中的第二份，该论文涉及相对双曲线组中局部极限定理。在第二篇论文中，我们将注意力限制在非光谱的随机步行中，我们证明了概率$ p_n（e，e）$的精确渐近造型，以回到时间$ n $。我们将改编自热力学形式主义的技术与第一张论文给出的绿色功能的粗略估计，以表明$ p_n（e，e）\ sim cr^{ - n} n} n^{ - 3/2} $，其中$ r $是随机步行的频谱半径。这概括了W. Woess的免费产品的结果，并且双曲线组的gou {ë} Zel的结果。
This is the second of a series of two papers dealing with local limit theorems in relatively hyperbolic groups. In this second paper, we restrict our attention to non-spectrally degenerate random walks and we prove precise asymptotics of the probability $p_n(e, e)$ of going back to the origin at time $n$. We combine techniques adapted from thermodynamic formalism with the rough estimates of the Green function given by the first paper to show that $p_n(e, e) \sim CR^{-n} n^{-3/2}$ , where $R$ is the spectral radius of the random walk. This generalizes results of W. Woess for free products and results of Gou{ë}zel for hyperbolic groups.
