Fourier decay, Renewal theorem and Spectral gaps for random walks on split semisimple Lie groups
Dynamical Systems
2020-04-28 v2 Probability
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.
Keywords
Cite
@article{arxiv.1811.06484,
title = {Fourier decay, Renewal theorem and Spectral gaps for random walks on split semisimple Lie groups},
author = {Jialun Li},
journal= {arXiv preprint arXiv:1811.06484},
year = {2020}
}
Comments
Major changes according to referee's report