Kazhdan–Margulis theorem for invariant random subgroups

Tsachik Gelander

doi:10.1016/j.aim.2017.06.011

Kazhdan–Margulis theorem for invariant random subgroups

Tsachik Gelander

Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

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 U_ϵ⊂G which intersects trivially the stabilizers of 1−ϵ of the points in every non-atomic probability G-space.

Original language	English (US)
Pages (from-to)	47-51
Number of pages	5
Journal	Advances in Mathematics
Volume	327
DOIs	https://doi.org/10.1016/j.aim.2017.06.011
State	Published - Mar 17 2018

Keywords

Invariant random subgroups
Kazhdan–Margulis theorem
Weakly uniformly discrete

ASJC Scopus subject areas

Mathematics(all)

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10.1016/j.aim.2017.06.011

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abstract = "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.",

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AB - 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.

KW - Invariant random subgroups

KW - Kazhdan–Margulis theorem

KW - Weakly uniformly discrete

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JF - Advances in Mathematics

ER -

Kazhdan–Margulis theorem for invariant random subgroups

Abstract

Keywords

ASJC Scopus subject areas

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