The central limit theorem for Markov chains started at a point

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Recent progress on the Random Conductance Model (2011, background): “Another approach goes by imposing decay-rate conditions on time-correlations (e.g., Maxwell and Woodroofe [103], Derriennic and Lin [47], Peligrad and Utev [113], Klicnarová and Volný [88], Volný [133], etc.).”
A new maximal inequality and invariance principle for stationary sequences (2004, result): “(3) In the ergodic case, Theorem 1.1 improves upon the corresponding results of Maxwell and Woodroofe (2000) [see also Derriennic and Lin (2003) and Wu and Woodroofe (2002)].”
Recent advances in invariance principles for stationary sequences (2006, methodology): “28 4.4.1 Linear processes and general normalization. . . . . . . . . 28 4.4.2 Strongly mixing sequences and general normalization . . . 31 References 32”
Pointwise ergodic theorems with rate and application to limit theorems for stationary processes (2009, methodology): “In particular, we will be interested in the Law of the Iterated Logarithm or,in the case where {Xn} is given by the functional of a Markov chain, in the quenched Central Limit Theorem.”
Synchronization (2018, unknown): “For a real parameter P 0 > 0 , define Then (1.1) holds and we have”