An entropic proof of cutoff on Ramanujan graphs
arXiv:2009.00837
Abstract
It is recently proved by Lubetzky and Peres that the simple random walk on a Ramanujan graph exhibits a cutoff phenomenon, that is to say, the total variation distance of the random walk distribution from the uniform distribution drops abruptly from near to near . There are already a few alternative proofs of this fact. In this note, we give yet another proof based on functional analysis and entropic consideration.
9 pages; Added remarks and references (v2)