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It is recently proved by Lubetzky and Peres that the simple random walk on aRamanujan graph exhibits a cutoff phenomenon, that is to say, the totalvariation distance of the random walk distribution from the uniformdistribution drops abruptly from near $1$ to near $0$. There are already a fewalternative proofs of this fact. In this note, we give yet another proof basedon functional analysis and entropic consideration.

An entropic proof of cutoff on Ramanujan graphs