A $k$-uniform hypergraph $G$ of size $n$ is said to be $\varepsilon$-far from having an independent set of size $\rho n$ if one must remove at least $\varepsilon n^k$ edges of $G$ in order for the remaining hypergraph to have an independent set of size $\rho n$. In this work, ... more >>>

We give a new method for analysing the mixing time of a Markov chain using
path coupling with stopping times. We apply this approach to two hypergraph
problems. We show that the Glauber dynamics for independent sets in a
hypergraph mixes rapidly as long as the maximum degree $\Delta$ of ... more >>>

In this paper we examine the importance of the choice of metric in path coupling, and the relationship of this to \emph{stopping time analysis}. We give strong evidence that stopping time analysis is no more powerful than standard path coupling. In particular, we prove a stronger theorem for path coupling ... more >>>