Invariant random subgroups over non-Archimedean local fields

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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
Early online date20 Oct 2018
StatePublished - 1 Dec 2018

All Science Journal Classification (ASJC) codes

  • General Mathematics


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