Central Limit Theorem for Sequential Dynamical Systems

The paper proves two characteristic-function approximations (Theorems 2.6 and 2.7) under hypotheses (C-1)–(C-4), (O-1)–(O-3), using twisted transfer operators, cone contraction (Hilbert metric), and a logarithmic blocking scale. The candidate solution follows the same framework: it writes the characteristic function as an iterated product of twisted transfer operators, performs a second-order expansion with Duhamel/telescoping, invokes uniform cone contraction to obtain exponential decorrelation, and implements a block splitting at scale L ≍ ln σ_n to control near/far interactions. It then derives the same bounds as in Theorem 2.6 and, under (O-3), the same analytic error and derivative bounds as in Theorem 2.7. Minor presentation gaps (e.g., explaining the precise origin of the (ln σ_n)^2 factor) do not affect the conclusion. Overall, the methods and results are essentially the same.