Markov duality and Bethe ansatz formula for half-line open ASEP

TL;DR

This paper develops a Markov duality for half-line open ASEP, solves the resulting ODE system with Bethe ansatz, and derives integral formulas for moments, confirming predictions for stochastic heat equations with boundary conditions.

Contribution

It introduces a Markov duality for half-line open ASEP and derives explicit integral formulas for moments using Bethe ansatz, extending previous results to boundary cases.

Findings

Derived Markov duality for half-line open ASEP.

Solved ODE system using Bethe ansatz.

Obtained integral formulas for q-moments and confirmed predictions.

Abstract

Using a Markov duality satisfied by ASEP on the integer line, we deduce a similar Markov duality for half-line open ASEP and open ASEP on a segment. This leads to closed systems of ODEs characterizing observables of the models. In the half-line case, we solve the system of ODEs using Bethe ansatz and prove an integral formula for $q$-moments of the current at $n$ distinct spatial locations. We then use this formula to confirm predictions for the moments of the multiplicative noise stochastic heat equation on $\mathbb R_{>0}$ with Robin type boundary condition and we obtain new formulas in the case of a Dirichlet boundary condition.