Multiparticle space–time transitions in the totally asymmetric simple exclusion process

We study correlation functions of the totally asymmetric simple exclusion process (TASEP) in discrete time with backward sequential update. We prove a determinant formula for the generalized Green's function describing transitions between particle positions at given instants. As an example, we calculate the current correlation function, i.e., the joint probability distribution of times required by each particle to travel a given distance. An asymptotic analysis shows that current fluctuations converge to the Airy$_2$ process.