Exact solution of TASEP and variants with inhomogeneous speeds and memory lengths

TL;DR

This paper extends an explicit biorthogonalization method to analyze TASEP variants with inhomogeneous speeds and memory lengths, providing explicit formulas for their distributions and studying specific models within this framework.

Contribution

It introduces a generalized biorthogonalization approach applicable to TASEP variants with speed and memory heterogeneity, enabling explicit distribution formulas.

Findings

Derived Fredholm determinant formulas for new TASEP variants.

Analyzed models with different particle speeds and memory lengths.

Provided asymptotic analysis potential for these systems.

Abstract

In [arXiv:1701.00018, arXiv:2107.07984] an explicit biorthogonalization method was developed that applies to a class of determinantal measures which describe the evolution of several variants of classical interacting particle systems in the KPZ universality class. The method leads to explicit Fredholm determinant formulas for the multipoint distributions of these systems which are suitable for asymptotic analysis. In this paper we extend the method to a broader class of determinantal measures which is applicable to systems where particles have different jump speeds and different memory lengths. As an application of our results we study three particular examples: some variants of TASEP with two blocks of particles having different speeds, a version of discrete time TASEP which mixes particles with sequential and parallel update, and a version of sequential TASEP with a block of long memory particles placed at the bulk of the system.