Year: 2019
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Dinh, Tien-Cuong, Kaufmann, Lucas, Wu, Hao
Institution: National University of Singapore
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2945839290