Invariant random subgroups over non-Archimedean local fields

Tsachik Gelander*, Arie Levit

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Let G be a higher rank semisimple linear algebraic group over a non-Archimedean local field. The simplicial complexes corresponding to any sequence of pairwise non-conjugate irreducible lattices in G are Benjamini–Schramm convergent to the Bruhat–Tits building. Convergence of the relative Plancherel measures and normalized Betti numbers follows. This extends the work (Abert et al. in Ann Math 185(3):711–790, 2017) from real Lie groups to linear groups over arbitrary local fields. Along the way, various results concerning Invariant Random Subgroups and in particular a variant of the classical Borel density theorem are also extended.

Original languageEnglish
Pages (from-to)1503-1544
Number of pages42
JournalMathematische Annalen
Issue number3-4
StatePublished - 1 Dec 2018
Externally publishedYes


FundersFunder number
Israel Science Foundation2095/15


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