This article is published open access under our Subscribe to Open model.
Let be a -regular tree and let be a geometrically finite discrete subgroup of the group of automorphisms of . In this article, we prove an extreme value theorem on the distribution of geodesics in a non-compact quotient graph . Main examples of such graphs are quotients of a Bruhat–Tits tree by non-cocompact discrete subgroups of of a local field of positive characteristic.
We investigate, for a given time , the measure of the set of -equivalent classes of geodesics with distance at most from a sufficiently large fixed compact subset of up to time . We show that there exists a function such that for Bowen–Margulis measure on the space of geodesics and the critical exponent of ,
In fact, we obtain a precise formula for : there exists a constant depending on and such that
Cite this article
Sanghoon Kwon, Seonhee Lim, Limiting distribution of geodesics in a geometrically finite quotients of regular trees. Groups Geom. Dyn. 15 (2021), no. 1, pp. 35–55DOI 10.4171/GGD/590