We present a new framework to derandomise certain Markov chain Monte Carlo (MCMC) algorithms. As in MCMC, we first reduce counting problems to sampling from a sequence of marginal distributions. For the latter task, we introduce a method called coupling towards the past that can, in logarithmic time, evaluate one or a constant number of variables from a stationary Markov chain state. Since there are at most logarithmic random choices, this leads to very simple derandomisation. We provide two applications of this framework, namely efficient deterministic approximate counting algorithms for hypergraph independent sets and hypergraph colourings, under local lemma type conditions matching, up to lower order factors, their state-of-the-art randomised counterparts.

翻译：我们提出了一种新的框架，用于对特定马尔可夫链蒙特卡洛（MCMC）算法进行去随机化。如同MCMC方法一样，我们首先将计数问题简化为从一系列边际分布中进行采样。针对后一任务，我们引入了一种称为“向过去耦合”的方法，该方法能够在对数时间内评估静止马尔可夫链状态中的一个或常数个变量。由于最多存在对数量级的随机选择，这导致了非常简单的去随机化过程。我们提供了该框架的两个应用，即在满足局部引理类型条件（匹配其最先进随机对应方法的低阶因子）的情况下，针对超图独立集和超图着色的高效确定性近似计数算法。