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Pure and Applied Mathematics Quarterly
Volume 17 (2021)
Number 3
Special Issue in Honor of Duong H. Phong
Edited by Tristan Collins, Valentino Tosatti, and Ben Weinkove
Products of random matrices: a dynamical point of view
Pages: 933 – 969
DOI: https://dx.doi.org/10.4310/PAMQ.2021.v17.n3.a4
Authors
Abstract
We study products of random matrices in $\mathrm{SL}^2 (\mathbb{C})$ 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.
This work was supported by the NUS grants C-146-000-047-001, AcRF Tier 1 R- 146-000-248-114 and R-146-000-259-114.
Received 23 May 2019
Accepted 8 January 2020
Published 14 June 2021