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August 2022 Effective Discreteness Radius of Stabilizers for Stationary Actions
T. Gelander, A. Levit, G. A. Margulis
Michigan Math. J. 72: 389-438 (August 2022). DOI: 10.1307/mmj/20217209

Abstract

We prove an effective variant of the Kazhdan–Margulis theorem generalized to stationary actions of semisimple groups over local fields: the probability that the stabilizer of a random point admits a nontrivial intersection with a small r-neighborhood of the identity is at most βrδ for some explicit constants β,δ>0 depending only on the group. This is a consequence of a key convolution inequality. We deduce that vanishing at infinity of injectivity radius implies finiteness of volume. Further applications are the compactness of the space of discrete stationary random subgroups and a novel proof of the fact that all lattices in semisimple groups are weakly cocompact.

Dedication

Dedicated to Gopal Prasad on the occasion of his 75th birthday.

Citation

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T. Gelander. A. Levit. G. A. Margulis. "Effective Discreteness Radius of Stabilizers for Stationary Actions." Michigan Math. J. 72 389 - 438, August 2022. https://doi.org/10.1307/mmj/20217209

Information

Received: 11 April 2021; Revised: 17 July 2021; Published: August 2022
First available in Project Euclid: 2 August 2022

Digital Object Identifier: 10.1307/mmj/20217209

Subjects:
Primary: 22E40 , 22E46 , 22F30 , 57S30 , 60G10

Rights: Copyright © 2022 The University of Michigan

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Vol.72 • August 2022
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