Modified log-Sobolev Inequalities for Strongly Log-Concave Distributions

Mary Cryan, Heng Guo, Giorgos Mousa
2019 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)  
A . We show that the modified log-Sobolev constant for a natural Markov chain which converges to an r-homogeneous strongly log-concave distribution is at least 1/r. As a consequence, we obtain an asymptotically optimal mixing time bound for this chain. Applications include the bases-exchange random walk in a matroid.
doi:10.1109/focs.2019.00083 dblp:conf/focs/Cryan0M19 fatcat:ihrgvm6wsbgkrey3ia3ichfcrm