Exclusion Processes and boundary conditions

TL;DR

This paper introduces a generalized family of boundary conditions for exclusion processes, calculates their probabilities using Bethe ansatz, and shows their large-time behavior aligns with known diffusion-pushing processes.

Contribution

It generalizes boundary conditions for exclusion processes and demonstrates their asymptotic equivalence with diffusion-pushing models using Bethe ansatz.

Findings

Boundary conditions generalized for exclusion processes

Conditional probabilities computed via Bethe ansatz

Large-time behavior matches diffusion-pushing processes

Abstract

A family of boundary conditions corresponding to exclusion processes is introduced. This family is a generalization of the boundary conditions corresponding to the simple exclusion process, the drop-push model, and the one-parameter solvable family of pushing processes with certain rates on the continuum [1-3]. The conditional probabilities are calculated using the Bethe ansatz, and it is shown that at large times they behave like the corresponding conditional probabilities of the family of diffusion-pushing processes introduced in [1-3].