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Fourier decay, Renewal theorem and Spectral gaps for random walks on split semisimple Lie groups

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arxiv 1811.06484 v2 pith:VA6EGOUB submitted 2018-11-15 math.DS math.PR

classification math.DSmath.PR
keywords decayfourierrandomrenewaltheoremabelianbourgain-dyatlovcases
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We establish an exponential error term for the renewal theorem in the context of products of random matrices, which is surprising compared with classical abelian cases. A key tool is the Fourier decay of the Furstenberg measures on the projective spaces, which is a higher dimensional generalization of a recent work of Bourgain-Dyatlov.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$

    math.DS 2026-07 conditional novelty 7.0 of 10

    Patterson-Sullivan measures of convex co-compact Schottky groups of dimension δ>1/2 satisfy |μ̂(ξ)| ≲ |ξ|^{-δ(2δ-1)/((2δ+1)(3-δ))}.

  2. Fourier decay of equilibrium states and the Fibonacci Hamiltonian

    math.DS 2025-07 conditional novelty 7.0 of 10

    Power Fourier decay is proved for equilibrium states of nonlinear area-preserving Axiom A surface diffeomorphisms, giving positive lower Fourier dimension for certain C^{1+} self-conformal measures and for the Fibonac...

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