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arXiv · 1510.05423

Kazhdan-Margulis theorem for Invariant Random Subgroups

Tsachik Gelander
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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 $ε$ there is an identity neighbourhood $U$ which intersects trivially the stabilizers of $1-ε$ of the points in every non-atomic $G$-space.

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Tsachik Gelander. 2017-06-18. Kazhdan-Margulis theorem for Invariant Random Subgroups. https://arxiv.org/abs/1510.05423

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