Temporal central limit theorem for mixed-radix odometer discrepancy

Source 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.