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Matrix Random Products with Singular Harmonic Measure by Kaimanovich, Vadim A.; Prince, Vincent Le is a scholarly article available to read on EtoBox.

What is Matrix Random Products with Singular Harmonic Measure about?

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.

Author

Kaimanovich, Vadim A.; Prince, Vincent Le

Published

2008

Language

EN