This paper studies the generic behavior of k-tuples of elements for k≥2 in a proper group action with contracting elements, with applications toward relatively hyperbolic groups, CAT(0) groups and mapping class groups. For a class of statistically convex-cocompact action, we show that an exponential generic set of k elements for any fixed k≥2 generates a quasi-isometrically embedded free subgroup of rank k. For k=2, we study the sprawl property of group actions and establish that statistically convex-cocompact actions are statistically hyperbolic in the sense of M. Duchin, S. Lelièvre, and C. Mooney.
@article{10_4171_ggd_593,
author = {Suzhen Han and Wen-Yuan Yang},
title = {Generic free subgroups and statistical hyperbolicity},
journal = {Groups, geometry, and dynamics},
pages = {101--140},
year = {2021},
volume = {15},
number = {1},
doi = {10.4171/ggd/593},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/593/}
}
TY - JOUR
AU - Suzhen Han
AU - Wen-Yuan Yang
TI - Generic free subgroups and statistical hyperbolicity
JO - Groups, geometry, and dynamics
PY - 2021
SP - 101
EP - 140
VL - 15
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/593/
DO - 10.4171/ggd/593
ID - 10_4171_ggd_593
ER -
%0 Journal Article
%A Suzhen Han
%A Wen-Yuan Yang
%T Generic free subgroups and statistical hyperbolicity
%J Groups, geometry, and dynamics
%D 2021
%P 101-140
%V 15
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/593/
%R 10.4171/ggd/593
%F 10_4171_ggd_593
