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Dynamics, Geometry and Groups Seminar

Speaker: Francesco Cellarosi

Title: 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.  Under some conditions, 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. Joint work with Maria Avdeeva.