Matrix random products with singular harmonic measure

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Any Zariski dense countable subgroup of $SL(d,R)$ is shown to carry a non-degenerate finitely supported symmetric random walk such that its harmonic measure on the flag space is singular. The main ingredients of the proof are: (1) a new upper estimate for the Hausdorff dimension of the projections of the harmonic measure onto Grassmannians in $R^d$ in terms of the associated differential entropies and differences between the Lyapunov exponents; (2) an explicit construction of random walks with uniformly bounded entropy and Lyapunov exponents going to infinity.

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Probability, 60J50; 28A78, 37D25, 53C35

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http://salesiana.dossiersoluciones.com/handle/123456789/164354

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0807.1015
 http://arxiv.org/abs/0807.1015

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arXiv