论文标题
双曲线空间上非质量随机步行的大偏差原理
Large deviation principles for non-elementary random walks on hyperbolic spaces
论文作者
论文摘要
我们表明，在双曲空间的等轴测图组上，非元素随机步行的位移和翻译距离满足具有相同速率函数$ i $的大偏差原理。粗略地，这意味着存在函数$ i（t）$，这准确地预测了长度$ n $的随机乘积的翻译距离为$ tn $的概率的指数衰减率，而对于位移也是如此。这解决了关于随机基质产物光谱半径的大偏差原理的猜想的特殊情况。在第二部分中，我们仅根据关节稳定长度的确定性概念来表征速率函数的有效支持。最后，作为我们技术的副产品，我们推断出对一组异构体的渐近学的一些进一步的确定性结果。本文中的某些结果是由Boulanger同时独立地获得的，正如我们在引言中讨论的那样。
We show that the displacement and translation distance of non-elementary random walks on isometry groups of hyperbolic spaces satisfy large deviation principles with the same rate function $I$. Roughly, this means that there exists function $I(t)$ which accurately predicts the exponential decay rate of the probability that the translation distance of a random product of length $n$ is $tn$, and similarly for the displacement. This settles a special case of a conjecture concerning the large deviation principle for the spectral radius of random matrix products. In a second part, we give a characterization of the effective support of the rate function only in terms of the deterministic notion of joint stable length. Finally, as a by-product of our techniques, we deduce some further deterministic results on the asymptotics of a bounded set of isometries. Some of the results in this paper were obtained simultaneously and independently by Boulanger--Mathieu as we discuss in the introduction.
