Effective Erdős–Wintner for Cantor numeration systems via a trailing-window method
We prove explicit Erdős–Wintner bounds for Cantor numeration systems via a trailing-window decomposition. We temporarily discard the last block of digits (the “window”) and analyze the remaining prefix, viewed through a short-range Markov/window chain. The resulting Kolmogorov-distance estimate splits into three contributions: (i) a bridge loss coming from discarding the window; (ii) a variance-type tail term for the prefix; and (iii) a regime-dependent smoothing term (Esseen’s inequality, bound
