Spectral gap of positive operators and applications

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Transportation-information inequalities for Markov processes (2007, background): “See [46, 22] for related results and references on this subject.”
Examples of moderate deviation principle for diffusion processes (2005, background): “It would be noted that seeming simplicity of (1.4) is delusive with the exception of the eigenvalue gap case (in short EG, see Gong and Wu, [ 8 ]) for P (t) x (a corresponding scenario can be found in [4]).”
On hyperboundedness and spectrum of Markov operators (2014, background): “Several attempts have been made to find a counterexample or to prove Høegh-Krohn and Simon’s conjecture, but extra assumptions were always needed, see for instance the papers of Aida [6], Mathieu [7], Wu [8], Hino [9,10], Cattiaux [11], Wang [12], Gong and Wu [13] and the bibliographical comments gi”