关于距离平稳序列的速度
概率论
2020-01-01 v1
摘要
我们证明了一个距离平稳随机序列速度的公式，推广了Karlsson和Ledrappier的大数定律。一个特例是i.i.d.矩阵乘积最大Lyapunov指数的经典公式，但我们的结果在各种不同情境中有应用。在许多情形下它给出了估计速度的方法，在其他情形下则能得到与随机游走相关的逃逸测度的维数下降结果。我们展示了在带电导的平稳可逆随机树、Cayley图的Bernoulli边渗流以及余紧Fuchsian群上的随机游走中的应用。
引用
@article{arxiv.1912.12523,
title = {On the speed of distance stationary sequences},
author = {Matias Carrasco and Pablo Lessa and Elliot Paquette},
journal= {arXiv preprint arXiv:1912.12523},
year = {2020}
}
备注
This article overlaps the (almost twice as long) preprint arXiv:1710.00733 which will remain unpublished. Compared with said preprint the results on hyperbolic Poisson-Delaunay random walks have been removed, the exposition of the abstract formula for speed has been improved, and new applications of it are given