  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 $1$ to near $0$. 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.
