  We consider the biased card shuffling and the Asymmetric Simple Exclusion
Process (ASEP) on the segment. We obtain the asymptotic of their mixing times:
our result show that these two continuous-time Markov chains display cutoff.
Our analysis combines several ingredients including: a study of the
hydrodynamic profile for ASEP, the use of monotonic eigenfunctions, stochastic
comparisons and concentration inequalities.
