Title: ASEP on a Ring and Corner Transfer Matrices

Speaker: Travis Scrimshaw(Hokkaido University)

Abstract: ASEP is a “toy” model where fermionic particles move left and right on a discrete lattice. Here we consider the lattice on a circle in continuous time and construct the steady state solution using the Matrix Product Ansatz, which postulates the claim as a trace of a product of matrices. Our solution is given by constructing a corner transfer matrix (in the sense of Baxter) using a quantum oscillator valued 5 vertex model, but unlike in the usual cases, it does not have the usual weight conservation nor satisfy the Yang-Baxter equation. Despite this, it retains enough structure to incorporate the multiline queuing process of Corteel-Mandelshtam-Williams and prove requisite relations. No knowledge will be assumed. This is based on joint work with Atsuo Kuniba and Masato Okado.