Lattices with and lattices without spectral gap

DOI10.4171/GGD/126zbMath1239.22003arXiv0909.1006MaRDI QIDQ664231

Alexander Lubotzky, Mohammed El Bachir Bekka

Publication date: 29 February 2012

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.1006

zbMATH Keywords

automorphism groups of treesspectral gap propertyexpander diagramslattices in algebraic groups

Mathematics Subject Classification ID

Ergodic theory on groups (22D40) Discrete subgroups of Lie groups (22E40) Ergodic theorems, spectral theory, Markov operators (37A30)

Related Items (5)

Effective mixing and counting in Bruhat–Tits trees ⋮ Ultrametric logarithm laws. II ⋮ Lattices in amenable groups ⋮ (Non)-escape of mass and equidistribution for horospherical actions on trees ⋮ Effective discreteness radius of stabilizers for stationary actions

Cites Work

• Hecke algebras from groups acting on trees and HNN extensions.
• Cusps of lattices in rank 1 Lie groups over local fields
• Tree lattices. With appendices by H. Bass, L. Carbone, A. Lubotzky, G. Rosenberg, and J. Tits.
• On uniqueness of invariant means
• A spectral gap property for subgroups of finite covolume in Lie groups

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