The authors prove theorems about the accuracy of asynchronous Gibbs sampling in graphical models with discrete variables that satisfy Dobrushin's condition. I am not familiar with this literature, so I'm taking the authors' description of the state of the literature as a given. The authors' results are as follows (let n be the number of variables in the graphical model, let t be the time index, and let tau be the maximum expected read delay in the asynchronous sampler): - Lemma 2. The asynchronous Gibbs sampler can be coupled to a synchronous Gibbs sampler with the same initial state such that the expected Hamming distance between them is bounded by O(tau*log(n)) uniformly in t. Lemma 3 gives an analogous bound for the dth moment of the Hamming distance. If a function f is K-Lipschitz with respect to the dth power of the Hamming distance, the bias of the asynchronous Gibbs sampler for the expectation of f is bounded by log d(n) (plus a constant, times a constant, and for sufficiently large t).