# On Benjamini--Schramm limits of congruence subgroups

## TL;DR

This paper proves that sequences of orbifolds derived from non-conjugate congruence lattices in higher rank semisimple groups over local fields of zero characteristic converge in the Benjamini--Schramm sense to their universal cover.

## Contribution

It establishes Benjamini--Schramm convergence for sequences of orbifolds associated with non-conjugate congruence lattices in higher rank semisimple groups.

## Key findings

- Sequences of orbifolds from non-conjugate congruence lattices are Benjamini--Schramm convergent.
- Convergence occurs to the universal cover in higher rank semisimple groups.
- Results apply to local fields of zero characteristic.

## Abstract

Every sequence of orbifolds corresponding to pairwise non-conjugate congruence lattices in a higher rank semisimple group over local fields of zero characteristic is Benjamini--Schramm convergent to the universal cover.