# Integral formulas of ASEP and $q$-TAZRP on a ring

## TL;DR

This paper derives explicit transition probability formulas for ASEP and q-TAZRP on a ring using coordinate Bethe ansatz, and computes the distribution of a tagged particle under general initial conditions.

## Contribution

It provides new integral formulas for ASEP and q-TAZRP on a ring, extending previous results to more general initial conditions.

## Key findings

- Explicit transition probability formulas for ASEP and q-TAZRP on a ring
- Distribution function for a tagged particle with general initial conditions
- Application of coordinate Bethe ansatz to these models

## Abstract

In this paper, we obtain the transition probability formulas for the Asymmetric Simple Exclusion Process (ASEP) and the $q$-deformed Totally Asymmetric Zero Range Process ($q$-TAZRP) on the ring by applying the coordinate Bethe ansatz. We also compute the distribution function for a tagged particle with general initial condition.