Interacting particle systems on the integer lattice that the coordinate Bethe Ansatz method can be applied to have connections to the random matrix theory and the symmetric function theory. We will survey the Bethe Ansatz method, and some known results and recent progresses in this direction. In particular, we will consider two initial configurations of the systems that are related to the GUE Tracy-Widom distribution and the GOE Tracy-Widom distribution.
The coordinate Bethe Ansatz solvable interacting particle systems
The coordinate Bethe Ansatz solvable interacting particle systems