Amenable equivalence relations and the construction of ergodic averages for group actions

L Bowen, A Nevo - Journal d'Analyse Mathématique, 2015 - Springer
We present a general new method for constructing pointwise ergodic sequences on
countable groups which is applicable to amenable as well as to non-amenable groups and …

Failure of the pointwise and maximal ergodic theorems for the free group

T Tao - Forum of Mathematics, Sigma, 2015 - cambridge.org
FAILURE OF THE L1 POINTWISE AND MAXIMAL ERGODIC THEOREMS FOR THE FREE
GROUP Page 1 Forum of Mathematics, Sigma (2015), Vol. 3, e27, 19 pages doi:10.1017/fms.2015.28 …

Convergence of spherical averages for actions of Fuchsian Groups

AI Bufetov, A Klimenko, C Series - arxiv preprint arxiv:1805.11743, 2018 - arxiv.org
Pointwise convergence of spherical averages is proved for a measure-preserving action of a
Fuchsian group. The proof is based on a new variant of the Bowen-Series symbolic coding …

von-Neumann and Birkhoff ergodic theorems for negatively curved groups

L Bowen, A Nevo - arxiv preprint arxiv:1303.4109, 2013 - arxiv.org
We prove maximal inequalities for concentric ball and spherical shell averages on a general
Gromov hyperbolic group, in arbitrary probability preserving actions of the group. Under an …

Convergence of spherical averages for actions of Fuchsian groups

AI Bufetov, A Klimenko, C Series - Commentarii Mathematici Helvetici, 2023 - ems.press
We prove pointwise convergence of spherical averages for a measure-preserving action of a
Fuchsian group. The proof is based on a new variant of the Bowen–Series symbolic coding …