  We survey recent results concerning the total-variation mixing time of the
simple exclusion process on the segment (symmetric and asymmetric) and a
continuum analog, the simple random walk on the simplex with an emphasis on
cutoff results. A Markov chain is said to exhibit cutoff if on a certain time
scale, the distance to equilibrium drops abruptly from $1$ to $0$. We also
review a couple of techniques used to obtain these results by exposing and
commenting some elements of proof.
