The Asymmetric Simple Exclusion Process, a Review

The asymmetric simple exclusion process  plays the role of  a
paradigm to study various aspects of non-equilibrium statistical physics.
It is a minimal model of interacting particles  with transport,
that displays  interesting  collective behaviour and breaks time-reversal
symmetry.  This system  appears as a building block in
more realistic descriptions of  low-dimensional transport with constraints.

 During the last twenty years, a large number of exact results
have been derived for the  exclusion process. We shall explain
the main techniques used to study this system
and some of the important results that have been obtained.