Double ergodicity of the Poisson boundary and applications to bounded cohomology

By Vadim A. Kaimanovich. 2003

98 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/af3244e68634bcdd1ebef3a72d805c55e4d0cf60

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The median class and superrigidity of actions on CAT(0) cube complexes (2012, background): “Furthermore, a strong Γ-boundary with properties (1) and (2) exists for any locally compact and compactly generated group according to [17], and for arbitrary locally compact groups with respect to a spread-out non-degenerate symmetric measure according to [34]; the existence of the boundary map wil”
Isometry groups of non‐positively curved spaces: discrete subgroups (2009, background): “For detailed background on this strengthening of ergodicity introduced in [20] and on the Poisson boundary in general, we refer the reader to [54].”
Isometric Embeddings in Bounded Cohomology (2013, background): “In that case, even to define the map Θ, it is necessary to use the fact that bounded cohomology can be computed via the complex of pluriharmonic functions [15], and that such a realization has no coboundaries in degree 2 due to the double ergodicity of the action of a group on an appropriate Poisson”
Bounded cohomology and isometry groups of hyperbolic spaces (2005, background): “2 that the assignment (g1,g2,g3) → ν(f)(g1x,g2x,g3x) (gi ∈ G) deﬁnes a G-equivariant cocycle with values in ℓp(G) whose cohomology class coincides with RΘ(f). Now by a result of Adams [A94] (see also [Ka03] for a more precise result), if σ is the measure class of the measure of maximal entropy for t”
Cocycle superrigidity and bounded cohomology for negatively curved spaces (2004, methodology): “We also make use of a measurable boundary construction introduced by Burger–Monod (loc. cit., later improved by Kaimanovich [25]), which enables us to apply boundary theory for general locally compact groups.”