Uniform Kazhdan Constants and Paradoxes of the Affine Plane

2019/04/04 by Pham, Lam · 2 citations
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1904.02604

Abstract

Let G=SL(2,ℤ)\ltimesℤ² and H=SL(2,ℤ). We prove that the action G\curvearrowrightℝ² is uniformly non-amenable and that the quasi-regular representation of G on ℓ²(G/H) has a uniform spectral gap. Both results are a consequence of a uniform quantitative form of ping-pong for affine transformations, which we establish here.

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• Uniform spectral gaps, non-abelian Littlewood-Offord and anti-concentration for random walks
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