Kazhdan–Margulis theorem for invariant random subgroups

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11 Scopus citations


Given a simple Lie group G, we show that the lattices in G are weakly uniformly discrete. This is a strengthening of the Kazhdan–Margulis theorem. Our proof however is straightforward — considering general IRS rather than lattices allows us to apply a compactness argument. In terms of p.m.p. actions, we show that for every ϵ>0 there is an identity neighbourhood Uϵ⊂G which intersects trivially the stabilizers of 1−ϵ of the points in every non-atomic probability G-space.

Original languageEnglish (US)
Pages (from-to)47-51
Number of pages5
JournalAdvances in Mathematics
StatePublished - Mar 17 2018


  • Invariant random subgroups
  • Kazhdan–Margulis theorem
  • Weakly uniformly discrete

ASJC Scopus subject areas

  • Mathematics(all)


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