A variety of paradigms have been proposed to speed up Markov chain mixing, ranging from non-backtracking random walks to simulated annealing and lifted Metropolis–Hastings. We provide a general characterization of the limits and opportunities of different approaches for designing fast mixing dynamics on graphs using the framework of “lifted Markov chains”. This common framework allows to prove lower and upper bounds on the mixing behavior of these approaches, depending on a limited set of assumptions on the dynamics. We find that some approaches can speed up the mixing time to diameter time, or a time inversely proportional to the graph conductance, while others allow for no speedup at all.

已经提出了各种范式来加快马尔可夫链的混合，从无回溯的随机游走到模拟的退火和提升都市圈-失速。我们提供了使用“提升马尔可夫链”框架设计图上快速混合动力学的不同方法的局限性和机会的一般表征。这个共同的框架可以证明这些方法的混合行为的上限和下限，这取决于对动力学的一组有限假设。我们发现有些方法可以将混合时间加快到直径时间，或者将时间与图形电导成反比，而另一些方法则根本不允许加速。