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The aim of this work is to give an introduction to the theoretical background and computational complexity of Markov chain Monte Carlo methods. Most of the mathematical results related to the convergence are not found in most of the statistical references, and computational complexity is still an open question for most of the MCMC methods. In this work, we provide a general overview, references, and discussion about all these theoretical subjects.arXiv:2004.07083v1 fatcat:zpahbc65bncdtchrkt5abawrwe