Non-equilibrium Dynamics and Random Matrices

We discuss some properties of a version of the one-dimensional totally asymmetric zero-range process in which a particle hops to the nearest neighbor site with rate proportional to \(1-q^n\), with \(n\) being the number of particles at the site. The process was introduced in 1998 by Wadati and the speaker as an integrable stochastic process but is recently studied in much more detail as a "good" discretization of the KPZ equation.