One-dimensional partially asymmetric simple exclusion process with open boundaries: Orthogonal polynomials approach

One-dimensional asymmetric simple exclusion process with open boundarys is considered. This is a kind of lattice gas model. Particles enter the system at left edge, diffuse asymmetrically in the bulk and leave out of the sysytem at right edge. They are also subject to the hard-core exclusion interaction. It has been known that the steady state properties of the model depends crutially on the boundary conditions. This boundary induced phase transition is explained from the point of view of the orthogonal polynomials.