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 Δ satisfies Δ≤ c 2^k/2, improving on the previous bound [BDK06] of Δ≤ k-2. This result brings the algorithmic bound to within a constant factor of the hardness bound of [BGG+16] which showed that it is NP-hard to approximately count independent sets on hypergraphs when Δ≥ 5 · 2^k/2.