Non-intersecting Path Constructions for TASEP with Inhomogeneous Rates and the KPZ Fixed Point

Abstract We consider a discrete-time TASEP, where each particle jumps according to Bernoulli random variables with particle-dependent and time-inhomogeneous parameters. use the combinatorics of Robinson–Schensted–Knuth correspondence certain intertwining relations express transition kernel this interacting system in terms ensembles weighted, non-intersecting lattice paths and, consequently, as marginal determinantal point process. next joint distribution positions Fredholm determinant, whose correlation is given boundary-value problem for discrete heat equation. The solution such finally leads us representation walk hitting probabilities, generalizing formulation Matetski et al. (Acta Math. 227(1):115–203, 2021) case both particle- rates. boundary value fully inhomogeneous appears finer structure than homogeneous case.