A systematic way to find and construct exact finite dimensional matrix   product stationary states
  We explain how to construct matrix product stationary states which are composed of finite-dimensional matrices. Our construction explained in this article was first presented in a part of [Hieida and Sasamoto:J. Phys. A: Math. Gen. 37 (2004) 9873] for general models. In this article, we give more details on the treatment than in the above-mentioned reference, for one-dimensional asymmetric simple exclusion process(ASEP). 
Yasuhiro Hieida (Saga University) and Tomohiro Sasamoto (Chiba   University)
cond-mat.stat-mech