14 citations · 32 across the 11 of their papers we have counts for
4 papers · 1 filter
Fine asymptotic geometry in the Heisenberg group
Moon Duchin, Christopher Mooney
For every finite generating set on the integer Heisenberg group H(Z), Pansu showed that the word metric has the large-scale structure of a Carnot-Caratheodory Finsler metric on the…
Statistical hyperbolicity in groups
Moon Duchin, Samuel Lelièvre, Christopher Mooney
In this paper, we introduce a geometric statistic called the "sprawl" of a group with respect to a generating set, based on the average distance in the word metric between pairs of…
The geometry of spheres in free abelian groups
Moon Duchin, Samuel Lelièvre, Christopher Mooney
We study word metrics on Z^d by developing tools that are fine enough to measure dependence on the generating set. We obtain counting and distribution results for the words of leng…
Generalizing the Croke-Kleiner Construction
Christopher Mooney
It is well known that every word hyperbolic group has a well-defined visual boundary. An example of C. Croke and B. Kleiner shows that the same cannot be said for CAT(0) groups. Al…