@inbook{37e1e8b2637f4942b3ec4742950edf9e,
title = "Variance Growth, Center-Tightness, and the Central Limit Theorem",
abstract = "We analyze the variance of S-N = f(1)(X-1, X-2) + center dot center dot center dot + f(N)(X-N, XN+1), , and characterize the additive functionals for which Var(S-N) negated right arrow infinity . Then we prove Dobrushins theorem: If Var(S-N) -> infinity, then S-N satisfies the central limit theorem.",
author = "Dmitry Dolgopyat and Sarig, \{Omri M.\}",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.",
year = "2023",
month = aug,
day = "1",
doi = "10.1007/978-3-031-32601-1\_3",
language = "English",
isbn = "978-3-031-32600-4",
volume = "2331",
series = "Lecture Notes in Mathematics",
publisher = "Springer Science and Business Media B.V.",
pages = "47--83",
booktitle = "Local Limit Theorems For Inhomogeneous Markov Chains",
address = "Germany",
}