PreprintCC BY 4.0arXiv
Temporal central limit theorem for mixed-radix odometer discrepancy
Abstract
We consider the local discrepancy for the number of visits of the orbit of $0$ under a mixed-radix odometer to intervals near the origin. Both the length of the orbit and the endpoint of the visited interval are chosen independently and uniformly at random. Under a Feller-type condition and an explicit condition ensuring that the finite random-time clock can be approximated by a Haar clock on the fluctuation scale, we obtain a temporal central limit theorem for the discrepancy, with an explicit Kolmogorov-Smirnov rate of convergence. This extends and strengthens the fixed-base temporal central limit theorem of Levin and Merzbach to the mixed-radix setting.
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BibTeX
@misc{avdeeva2026temporal,
title = {{Temporal central limit theorem for mixed-radix odometer discrepancy}},
author = {Maria Avdeeva and Francesco Cellarosi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34243},
eprint = {2610.34243},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34243},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Temporal central limit theorem for mixed-radix odometer discrepancy
AU - Maria Avdeeva
AU - Francesco Cellarosi
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34243
UR - https://arxiv.org/abs/2610.34243
AB - We consider the local discrepancy for the number of visits of the orbit of $0$ under a mixed-radix odometer to intervals near the origin. Both the length of the orbit and the endpoint of the visited interval are chosen independently and uniformly at random. Under a Feller-type condition and an explicit condition ensuring that the finite random-time clock can be approximated by a Haar clock on the fluctuation scale, we obtain a temporal central limit theorem for the discrepancy, with an explicit Kolmogorov-Smirnov rate of convergence. This extends and strengthens the fixed-base temporal central limit theorem of Levin and Merzbach to the mixed-radix setting.
ER -