Rapid mixing of hypergraph independent sets

We prove that the mixing time of the Glauber dynamics for sampling independent sets on n‐vertex k‐uniform hypergraphs is O(nlogn) when the maximum degree Δ satisfies Δ ≤ c2k/2, improving on the previous bound Bordewich and co‐workers of Δ ≤ k − 2. This result brings the algorithmic bound to within a constant factor of the hardness bound of Bezakova and co‐workers which showed that it is NP‐hard to approximately count independent sets on hypergraphs when Δ ≥ 5·2k/2.