On the rate of convergence in the entropic central limit theorem

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Log-Concavity and Strong Log-Concavity: a review (2014, background): “…beginnings in the work of Linnik (1959), Brown (1982), and Barron (1986), but has interesting cross-connections with log-concavity in the more recent papers of Johnson and Barron (2004), Carlen and Soffer (1991), Ball, Barthe and Naor (2003), Artstein et al. (2004a), and Artstein et al. (2004b).”
On Kac's chaos and related problems (2012, unknown): “of the local CLT have been established corresponding to different regularity assumption made on the probability g, we refer the interested reader to the recent works [57], [8], [3] and the references therein.”
Relative entropy of cone measures and Lp centroid bodies (2009, background): “ng and Zhang [20, 37, 38, 39, 40]) use Lp Brunn Minkowski theory to develop certain entropy inequalities. Also, classical Brunn Minkowski theory is related to information theoretic concepts (see e.g. [3, 4, 5, 6, 14, 15]. An important aﬃne invariant quantity in convex geometric analysis is the aﬃne ”
Rényi divergence and the central limit theorem (2016, background): “erent aspects of such strong CLT’s, including the non-i.i.d. situation and the problem of rates or Berry-Esseen bounds, were studied by many authors, and we refer an interested reader to [Li], [S-M], [A-B-B-N], [B-J], [J], [B-C-G2-4], [B-C-K], [B-C]. As for convergence in Dα with α>1, not much is”