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

Guillaume Barraquand and Ivan Corwin
Vol. 5 (2024), No. 1, 89–129
DOI: 10.2140/pmp.2024.5.89
Abstract

Using a Markov duality satisfied by ASEP on the integer line, we deduce similar dualities 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 integrated 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 ℝ>0 with Robin type boundary condition and we obtain new formulas in the case of a Dirichlet boundary condition.

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Keywords
integrable probability, interacting particle systems, Markov duality, Kardar–Parisi–Zhang equation
Mathematical Subject Classification
Primary: 60J27, 82B23, 82C22
Secondary: 60H15
Milestones
Received: 9 January 2023
Revised: 24 November 2023
Accepted: 26 December 2023
Published: 30 January 2024
Authors
Guillaume Barraquand
Laboratoire de Physique de l’Ecole Normale Supérieure
ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité
Paris
France
Ivan Corwin
Department of Mathematics
Columbia University
New York, NY
United States
© 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers).