On effective equidistribution for product-type self-affine measures

Han Zhang

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arXiv · 2610.22001

On effective equidistribution for product-type self-affine measures

Han Zhang

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Abstract

We establish an effective equidistribution theorem on homogeneous spaces for expanding translates of product-type self-affine measures seen on unipotent orbits along any sequence of diagonal elements drifting away from walls. In particular, we do not require the diagonal elements to lie in a fixed proper and closed subcone. The main new ingredients in the proof of our equidistribution theorem include an adaptation of the methods in \cite{BHZ25} to the setting of product-type self-affine measures, as well as a weighted effective recurrence theorem for intertwined associated random walks. The latter involves decomposing the random walks according to suitable stopping times and applications of intertwined Benoist-Quint height functions.

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Han Zhang. 2026-10-15. On effective equidistribution for product-type self-affine measures. https://arxiv.org/abs/2610.22001

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