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Khintchine dichotomy for images of self-similar measures and almost random walks
Abstract
Following the celebrated breakthrough in Bénard-He-Zhang, we prove Khintchine dichotomy for push-forwards of self-similar measures on ℝd under uniform C1+α maps. For this, we also study almost random walks on SL(d+1,ℝ)/SL(d+1,ℤ) and prove their effective equidistribution.
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BibTeX
@misc{shao2026khintchine,
title = {{Khintchine dichotomy for images of self-similar measures and almost random walks}},
author = {Liyang Shao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13099},
eprint = {2610.13099},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13099},
}
RIS
TY - UNPB
TI - Khintchine dichotomy for images of self-similar measures and almost random walks
AU - Liyang Shao
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.13099
UR - https://arxiv.org/abs/2610.13099
AB - Following the celebrated breakthrough in Bénard-He-Zhang, we prove Khintchine dichotomy for push-forwards of self-similar measures on ℝ^d under uniform C^1+α maps. For this, we also study almost random walks on SL(d+1,ℝ)/SL(d+1,ℤ) and prove their effective equidistribution.
ER -