caa a22 4500 445884487 CHVBK 20180317145555.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s10711-010-9504-9 doi (NATIONALLICENCE)springer-10.1007/s10711-010-9504-9 Matrix random products with singular harmonic measure [Elektronische Daten] [Vadim Kaimanovich, Vincent Le Prince] Any Zariski dense countable subgroup of $${SL(d, \mathbb {R})}$$ 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 $${\mathbb {R}^d}$$ 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 arbitrarily long Lyapunov vector. Springer Science+Business Media B.V., 2010 Random walk nationallicence Matrix random product nationallicence Lyapunov exponents nationallicence Harmonic measure nationallicence Hausdorff dimension nationallicence Kaimanovich Vadim Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, K1N 6N5, Ottawa, ON, Canada aut Le Prince Vincent IRMAR, Université Rennes-1, Campus de Beaulieu, 35042, Rennes, France aut Geometriae Dedicata Springer Netherlands 150/1(2011-02-01), 257-279 0046-5755 150:1<257 2011 150 10711 https://doi.org/10.1007/s10711-010-9504-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9504-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kaimanovich Vadim Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, K1N 6N5, Ottawa, ON, Canada aut NATIONALLICENCE 700 1- Le Prince Vincent IRMAR, Université Rennes-1, Campus de Beaulieu, 35042, Rennes, France aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 150/1(2011-02-01), 257-279 0046-5755 150:1<257 2011 150 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer