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

Jialun Li

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arXiv · 1811.06484

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

Jialun Li

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Abstract

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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Jialun Li. 2018-11-15. Fourier decay, Renewal theorem and Spectral gaps for random walks on split semisimple Lie groups. https://arxiv.org/abs/1811.06484

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