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Random products of matrices: a dynamical point of view
Tien-Cuong Dinh, Lucas Kaufmann, Hao Wu · 2019-05-21 · via math.PR updates on arXiv.org

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.

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