A deviation inequality for non-reversible Markov processes

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CURVATURE, CONCENTRATION AND ERROR ESTIMATES FOR MARKOV CHAIN MONTE CARLO (2009, unknown): “The Annals of Probability 2010, Vol. 38, No. 6, 2418–2442 DOI: 10.1214/10-AOP541 © Institute of Mathematical Statistics, 2010”
Transportation cost-information inequalities and applications to random dynamical systems and diffusions (2004, background): “See [21] for the nonadaptability of the log-Sobolev inequality w.”
A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature (2009, background): “On the other hand, it is classical that such a functional inequality entails a similar Gaussian decay to that given above; see, for instance, Wu (2000) or the recent article of Guillin et al. (2009).”
Transportation-information inequalities for Markov processes (2007, background): “It is proved in [43, 44] that in the symmetric case, Iu(r) is exactly the rate function governing the large deviation principle of 1 t ∫ t 0 u(Xs) ds for bounded u.”
Bernstein type's concentration inequalities for symmetric Markov processes (2010, unknown): “(1.1)”