Rapid Mixing of Hypergraph Independent Set

We prove that the the mixing time of the Glauber dynamics for sampling independent sets on $n$-vertex $k$-uniform hypergraphs is $O(nlog n)$ when the maximum degree $Delta$ satisfies $Delta leq c 2^{k/2}$, improving on the previous bound [BDK06] of $Delta leq k-2$. This result brings the algorithmic bound to within a constant factor of th...More