Stationary measures of the KPZ equation on an interval from Enaud–Derrida’s matrix product ansatz representation
Guillaume Barraquand, Pierre Le Doussal
Abstract
Abstract The stationary measures of the Kardar–Parisi–Zhang equation on an interval have been computed recently. We present a rather direct derivation of this result by taking the weak asymmetry limit of the matrix product ansatz for the asymmetric simple exclusion process. We rely on the matrix product ansatz representation of Enaud and Derrida, which allows to express the steady-state in terms of re-weighted simple random walks. In the continuum limit, its measure becomes a path integral (or re-weighted Brownian motion) of the form encountered in Liouville quantum mechanics, recovering the recent formula.
Topics & Concepts
AnsatzAsymmetric simple exclusion processPath integral formulationLimit (mathematics)MathematicsMatrix multiplicationProduct (mathematics)Matrix (chemical analysis)Mathematical physicsBrownian motionRepresentation (politics)Measure (data warehouse)Statistical physicsQuantumMathematical analysisQuantum mechanicsPhysicsStatisticsDatabasePolitical sciencePoliticsLawMaterials scienceComputer scienceComposite materialGeometryRandom Matrices and ApplicationsStochastic processes and statistical mechanicsTheoretical and Computational Physics