Equidistribution, ergodicity and irreducibility associated with Gibbs measures
Adrien Boyer
The Weizmann Institute of Science, Rehovot, IsraelDustin Mayeda
The Weizmann Institute of Science, Rehovot, Israel
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Abstract
We generalize an equidistribution theorem à 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 inspired by a result of Roblin. In particular, we deduce irreducibility of these new classes of boundary representations.
Cite this article
Adrien Boyer, Dustin Mayeda, Equidistribution, ergodicity and irreducibility associated with Gibbs measures. Comment. Math. Helv. 92 (2017), no. 2, pp. 349–387
DOI 10.4171/CMH/414