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- Nonetheless, these standards require some second condition on the measure μ\mu (finite first second for ray approximation, finite logarithmic moment for the strip approximation) to control the geometry of the random walk.
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Nevertheless, these criteria require some moment situation on the measure μ\mu (finite first moment for ray approximation, finite logarithmic moment for the strip approximation) to control the geometry of the random walk. Later, Kaimanovich Kai00 prolonged this identification outcome, between the Poisson boundary of the discrete group and the Furstenberg boundary of the ambient Lie group, to the more general case that μ\mu has finite entropy and finite logarithmic moment. We do not assume any moment situation on the random stroll and, in contrast with the previous rank 11 proof, we do not depend on pivoting theory.
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