I will present a modified log-Sobolev inequality for r-homogeneous strongly log-concave distributions. As a consequence, we obtain an asymptotically optimal mixing time bound for the bases-exchange chain, and a concentration result for such distributions. The proof is simple and elementary. No functional analysis is involved.
(Joint work with Mary Cryan and Giorgos Mousa.)
Heng Guo is a lecturer in the University of Edinburgh. He came to Edinburgh after spending two years in Berkeley and London. Before that, he completed his Ph.D. in the University of Wisconsin - Madison in 2015, which has won the EATCS Distinguished Dissertation award.