A Note on Complex-Hyperbolic Kleinian Groups

Dey, Subhadip; Kapovich, Michael

doi:10.1007/s40598-020-00143-x

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Boundary Actions Of Hyperbolic Groups and Stable Fields2

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2022

2024

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Cited by 3 publications

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“…Fundamental work of Labourie [24] and Guichard-Wienhard [19] shows that the limit set Λ G is homeomorphic to the Gromov boundary ∂ G G in this case. Dey and Kapovich [13] prove that the Patterson-Sullivan measure turns out to be a conformal density with certain uniqueness properties in this case. See [13].…”

Section: Boundary Actions Of Hyperbolic Groups and Stable Fieldsmentioning

confidence: 92%

See 1 more Smart Citation

Mixing Properties of Stable Random Fields Indexed by Amenable and Hyperbolic Groups

Mj¹,

Roy²,

Sarkar³

2022

Preprint

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We show that any stationary symmetric α-stable (SαS) random field indexed by a countable amenable group G is weakly mixing if and only if it is generated by a null action, extending works of Samorodnitsky and Wang-Roy-Stoev for abelian groups to all amenable groups. This enables us to improve significantly the domain of a recently discovered connection to von Neumann algebras. We also establish ergodicity of stationary SαS fields associated with boundary and double boundary actions of a hyperbolic group G, where the boundary is equipped with either the Patterson-Sullivan or the hitting measure of a random walk, and the double boundary is equipped with the Bowen-Margulis-Sullivan measure.

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Section: Boundary Actions Of Hyperbolic Groups and Stable Fieldsmentioning

confidence: 92%

“…Dey and Kapovich [13] prove that the Patterson-Sullivan measure turns out to be a conformal density with certain uniqueness properties in this case. See [13].…”

Section: Boundary Actions Of Hyperbolic Groups and Stable Fieldsmentioning

confidence: 92%