Limiting Distribution of Dense Orbits in a Moduli Space of Rank m Discrete Subgroups in (m+1)-Space

Abstract We study the limiting distribution of dense orbits of a lattice subgroup SL (m+1, R) acting on H SL (m+1, R), with respect to a filtration of growing norm balls. The novelty of our work is that the groups H we consider have infinitely many non-trivial connected components. For a specific such H, the homogeneous space H G identifies with X₌, ₌+₁, a moduli space of rank m-discrete subgroups in R^m+1. This study is motivated by the work of Shapira-Sargent who studied random walks on X₂, ₃.