Random products of matrices: a dynamical point of view
Complex Variables
2019-05-22 v1 Dynamical Systems
Probability
Abstract
We study random products of matrices in SL_2(C) from the point of view of holomorphic dynamics. For non-elementary measures with finite first moment we obtain the exponential convergence towards the stationary measure in Sobolev norm. As a consequence we obtain the exponentially fast equidistribution of forward images of points towards the stationary measure. We also give a new proof of the Central Limit Theorem for the norm cocycle under a second moment condition, originally due to Benoist-Quint, and obtain some general regularity results for stationary measures.
Keywords
Cite
@article{arxiv.1905.08461,
title = {Random products of matrices: a dynamical point of view},
author = {Tien-Cuong Dinh and Lucas Kaufmann and Hao Wu},
journal= {arXiv preprint arXiv:1905.08461},
year = {2019}
}
Comments
27 pages