Mathematics

I will discuss the relation between non-compact spin chains studied in high energy physics and the zero-range processes introduced by Sasamoto-Wadati, Povolotsky and Barraquand-Corwin. The main difference compared to the standard SSEP and ASEP is that in these models several particles can occupy one and the same site. For the models with symmetric hopping rates I will introduce integrable boundary conditions that are obtained from new solution to the boundary Yang-Baxter equation (K-matrix). An explicit mapping of the open SSEP (and the non-compact model cousin) to equilibrium is presented. It allows to obtain closed-form solutions of the probabilities in steady state and of k-point correlations function.