bibkey: “janson2021mdependent” authors: “Svante Janson” year: 2021 title: “A central limit theorem for m-dependent variables” doi: “10.48550/arXiv.2108.12263” url: “https://arxiv.org/abs/2108.12263v1” claim: “A centered m-dependent triangular array satisfies a central limit theorem under a Lindeberg condition; for fixed dependence range, a vanishing Lyapunov ratio with any moment order greater than two suffices.” strata_touched: [] license: “citation-only” triage: “anchor”

A central limit theorem for m-dependent variables

The inspected source is arXiv:2108.12263v1 (27 August 2021), 12 pages. Theorem 1.1, page 1, states the central limit theorem for a fixed dependence range and centered, square-integrable triangular arrays with positive row-sum variance and the usual Lindeberg condition. Theorem 4.1, page 7, gives the Lyapunov form: for moment order p > 2, dependence range m_N, and row-sum standard deviation sigma_N, it suffices that m_N^(p-1) sum_i E|X_Ni|^p / sigma_N^p -> 0. For independent summands within each row, one may take dependence range one, as explained in Remark 1.5; range two applies to the path-edge arrays here.

This central limit theorem is literature-attested. The parity-kernel application must separately establish the two-step reset under the normalized double likelihood tilt, compare its uniform and stationary initial laws, and bound its means, covariance matrix and absolute third moments uniformly over all amplitudes in (0,1). Those model-specific calculations and the resulting critical-window risk and recovery curves are repo-derived deductions. The source itself does not state those statistical experiments or curves.