Equidistribution, ergodicity and irreducibility associated with Gibbs measures

Adrien Boyer, Dustin Mayeda

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Abstract:We generalize an equidistribution theorem \`a la Bader-Muchnik for operator-valued measures constructed from a family of boundary representations associated with Gibbs measures in the context of convex cocompact discrete group of isometries of a simply connected connected Riemannian manifold with pinched negative curvature. We combine a functional analytic tool, namely the property RD of hyperbolic groups, together with a dynamical tool: an equidistribution theorem of Paulin, Pollicott and Schapira insp ...
Application of Property RD
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23 days ago
KeithM ▴ 40

How is property RD used in the proof of the main theorem?

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Dustin 125

It is used to prove the bound in proposition 4.6 which is then used crucially in proposition 4.7 to prove the uniform boundedness of the operators.

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