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arXiv · 2610.34243

Temporal central limit theorem for mixed-radix odometer discrepancy

Maria Avdeeva·Francesco Cellarosi
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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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Maria Avdeeva, Francesco Cellarosi. 2026-10-25. Temporal central limit theorem for mixed-radix odometer discrepancy. https://arxiv.org/abs/2610.34243

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