From the asymmetric simple exclusion processes to the stationary measures of the KPZ fixed point on an interval

Abstract

Barraquand and Le~Doussal introduced a family of stationary measures for the (conjectural) KPZ fixed point on an interval with Neumann boundary conditions, and predicted that they arise as scaling limit of stationary measures of all models in the KPZ universality class on an interval. In this paper, we show that the stationary measures for KPZ fixed point on an interval arise as the scaling limits of the height increment processes for the open asymmetric simple exclusion process in the steady state, with parameters changing appropriately as the size of the system tends to infinity.

References in corpus (5)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Markov processes related to the stationary measure for the open KPZ equation
• Markov limits of steady states of the KPZ equation on an interval
• The Doob-McKean identity for stable Lévy processes
• Some recent progress on the stationary measure for the open KPZ equation

Cited by in corpus (7)

• Approximating the stationary distribution of the ASEP with open boundaries
• KPZ fluctuations in finite volume
• Askey-Wilson signed measures and open ASEP in the shock region
• Fluctuations of random Motzkin paths II
• A two-line representation of stationary measure for open TASEP
• Approach to stationarity for the KPZ fixed point with boundaries
• Limit fluctuations of stationary measure of totally asymmetric simple exclusion process with open boundaries on the coexistence line