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On effective equidistribution for product-type self-affine measures
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.
Related
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BibTeX
@misc{zhang2026effective,
title = {{On effective equidistribution for product-type self-affine measures}},
author = {Han Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22001},
eprint = {2610.22001},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22001},
}
RIS
TY - UNPB
TI - On effective equidistribution for product-type self-affine measures
AU - Han Zhang
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22001
UR - https://arxiv.org/abs/2610.22001
AB - 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.
ER -