In this paper we consider the problem of sampling from the low-temperature exponential random graph model (ERGM). The usual approach is via Markov chain Monte Carlo, but strong lower bounds have been established for the ERGM showing that any local Markov chain suffers from an exponentially large mixing time due to metastable states. We instead consider \emph{metastable mixing}, a notion of approximate mixing within a collection of metastable states. In the case of the ERGM, we show that Glauber dynamics with the right $G(n,p)$ initialization has a metastable mixing time of $O(n^2\log n)$ to within total variation distance $\exp(-\Omega(n))$ to the ERGM.

翻译：在本文中,我们考虑了从低温指数随机图模型(ERGM)中取样的问题。通常的做法是通过Markov链Monte Carlo,但已经为ERGM确定了很强的下限,表明任何本地的Markov链因元化状态而具有指数性大混合时间。我们相反地认为\emph{metable mix},这是一种在元化状态集合中混合的近似概念。在ERGM中,我们显示,Glauber动态与右$G(n),p)的初始化具有可变混合时间为$O(n%2\log n)至ERGM总变异距离$(\\\Omega(n))美元($)。