We prove that the the mixing time of the Glauber dynamics for sampling independent sets on n-vertex k-uniform hypergraphs is Opn log nq when the maximum degree ∆ satisfies ∆ ď c2k{2, improving on the previous bound [BDK06] of ∆ ď 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 in...
