Approximations of "effective sample size" in Markov Chain Monte Carlo in textbooks generally seem to assume that the autocorrelation function of the MC in equilibrium decays sufficiently rapidly to dominate linear terms. It seems plausible based on processes like autoregressive models that autocorrelation should decay exponentially, but I am struggling to say anything concrete about markov chains in general.
Is there a way to set up some sort of dynamical sysyem to give some insight in to how autocorrelation must behave? Ideally this would be applicable to continuous state spaces but discrete or even finite would still be very insightful.