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- Measurable boundary maps and Patterson–Sullivan measures for non-Borel Anosov teams on the Furstenberg boundary (2026)
Nevertheless, these standards require some moment condition on the measure μ\mu (finite first moment for ray approximation, finite logarithmic second for the strip approximation) to manage the geometry of the random stroll. Later, Kaimanovich Kai00 extended this identification result, 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 do not assume any second condition on the random stroll and, in distinction with the earlier rank eleven proof, we do not depend on pivoting principle.
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Measurable boundary maps and Patterson–Sullivan measures for non-Borel Anosov teams on the Furstenberg boundary (2026) Continuous cochains on Furstenberg boundaries and injectivity of the comparison map (2025) Progress circumstances for freeness of the Furstenberg boundary motion (2026) For a minimal compact ∂FG\partial_F G∂FG11-space ∂FG\partial_F G∂FG12, a ∂FG\partial_F G∂FG13-boundary is a minimal strongly proximal extension ∂FG\partial_F G∂FG14, and the universal object ∂FG\partial_F G∂FG15 specializes to the classical Furstenberg boundary when ∂FG\partial_F G∂FG16 is a degree (Naghavi, 2019). For Zariski-dense subgroups of real linear semisimple algebraic teams, there is a distinctive stationary measure on G/PG/PG/P1, pattern paths converge to boundary factors with that legislation, and the G/PG/PG/P2-components in the Cartan decomposition turn out to be asymptotically impartial with exponential pace (Aoun, 2017). The Furstenberg boundary GGG0 is then characterised by the universal property
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