Axel Saenz Rodriguez: Fredholm determinant for the inhomogeneous TASEP

Abstract

The totally asymmetric simple exclusion process (TASEP) is a collection of random walkers with interactions so that particles never occupy the same site at the same time. This process was introduced in the late 60’s, in biology, by C.T. MacDonald, J.H. Gibbs, and A.C. Pipkin and, in math by, F. Spritzer. Recently, there has been some progress in accessing the asymptotic statistics of the TASEP via Fredholm determinant formulas. In this talk, I discuss joint work with Elia Bisi (TU Wien), Yuchen Liao (Warwick) and Nikos Zygouras (Warwick) where we obtain a random walk Fredholm determinant formula for the multi-point function of the TASEP under general initial conditions and inhomogeneous particle speeds.