STABLE CLT FOR DETERMINISTIC SYSTEMS

The paper proves that for every ergodic aperiodic probability-preserving system and every α in (0,2), there exists an observable f with n^{-1/α} S_n(f) converging in distribution to a symmetric α-stable law with any prescribed dispersion σ; see Theorem 1 and its proof, including the final rescaling to arbitrary σ . The candidate solution correctly invokes exactly this result and then (redundantly but harmlessly) rescales to match a target σ, and notes that convergence in distribution implies cdf convergence at all t because the limit law is non-atomic, as also noted in the paper’s preliminaries . The model’s write-up does not reproduce the paper’s constructive proof (triangular array, discretization, and embedding via the Alpern-lemma–independent partition), but it is a valid solution by citation.