However, these standards require some moment condition on the measure μ\mu (finite first moment for ray approximation, finite logarithmic second for the strip eco card casino approximation) to manage the geometry of the random walk. Later, Kaimanovich Kai00 extended this identification outcome, between the Poisson boundary of the discrete group and the Furstenberg boundary of the ambient Lie group, to the extra basic case that μ\mu has finite entropy and finite logarithmic second. We don’t assume any second condition on the random stroll and, in distinction with the previous rank eleven proof, we don’t depend on pivoting concept.

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