Poisson boundaries of discrete groups of matrices

DOI10.1007/BF02759763zbMath0574.60012MaRDI QIDQ1063925

François Ledrappier

Publication date: 1985

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Poisson boundaryDirac measurenatural boundaryentropy- conditionsOseledeč's theorem

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Discrete-time Markov processes on general state spaces (60J05) Probabilistic potential theory (60J45) Boundary theory for Markov processes (60J50) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items

Boundary and entropy of space homogeneous Markov chains ⋮ Convex-invariant means and a pathwise central limit theorem ⋮ Poisson boundary of groups acting on \(\mathbb R\)-trees. ⋮ Stationary \(C^\ast \)-dynamical systems (with an appendix by Uri Bader, Yair Hartman, and Mehrdad Kalantar) ⋮ Exact dimension of Furstenberg measures ⋮ Matrix random products with singular harmonic measure ⋮ Harmonic functions on infinite graphs ⋮ Dynamics on the space of 2-lattices in 3-space ⋮ Poisson boundary of \(GL_d (\mathbb Q)\) ⋮ Topology and dynamics of laminations in surfaces of general type ⋮ Poisson boundary of triangular matrices in a number field ⋮ Random walks on the discrete affine group ⋮ Random matrix products when the top Lyapunov exponent is simple

Cites Work

• A proof of Oseledec's multiplicative ergodic theorem
• Martin boundaries of random walks on Fuchsian groups
• Random walks on discrete groups: Boundary and entropy
• Ergodic theory of differentiable dynamical systems
• Discrete groups of motions of manifolds of nonpositive curvature
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