why do you need fast mixing chain why do we care about mixing in the markov chain? do you need mcmc to mix fast why should we care about rapid mixing in mcmc chains why should we care about rapid mixing in mcmc chains why we need to care about rapid mixing in mcmc why does monte carlo use rapid mixing how does the markov chain work why should you care about mixing in mcmc vs monte carlo why is the mcmc used in mcmc chains why should we care about rapid mixing of markov chains why do we need to care about mixing in markov chains why should mcmc chains mix quickly why do we care about mixing of mcmc in a chain why do chain operators care about fast mixing why do mcmc chains mix quickly why do you care about rapid mixing in mcmc why is rapid mixing needed in mcmc why does the chain need rapid mixing? why not to care about mixing