# Color-position symmetry in interacting particle systems

## TL;DR

This paper establishes a color-position symmetry in a class of discrete-time ASEP-like particle systems, enabling new insights into multi-species models and asymptotic behaviors of second class particles.

## Contribution

It introduces a novel symmetry for inhomogeneous ASEP-like systems, extending previous results to colored models and deriving new asymptotic behaviors.

## Key findings

- Proved color-position symmetry for a class of ASEP-like systems.
- Extended symmetry results to multi-species ASEP and vertex models.
- Discovered new asymptotic behaviors of second class particles.

## Abstract

We prove a color-position symmetry for a class of ASEP-like interacting particle systems with discrete time on the one-dimensional lattice. The full space-time inhomogeneity of our systems allows to apply the result to colored (or multi-species) ASEP and stochastic vertex models for a certain class of initial/boundary conditions, generalizing previous results of Amir-Angel-Valko and Borodin-Wheeler. We are also able to use the symmetry, together with previously known results for uncolored models, to find novel asymptotic behavior of the second class particles in several situations.