Weakly asymmetric bridges and the KPZ equation

Abstract

We consider the corner growth dynamics on discrete bridges from $(0,0)$ to $(2N,0)$, or equivalently, the weakly asymmetric simple exclusion process with $N$ particles on $2N$ sites. We take an asymmetry of order $N^{-\alpha }$ with $\alpha \in (0,1)$ and provide a complete description of the asymptotic behaviour of this model. In particular, we show that the hydrodynamic limit of the density of particles is given by the inviscid Burgers equation with zero-flux boundary condition. When the interface starts from the flat initial profile, we show that KPZ fluctuations occur whenever $\alpha \in (0,1/3]$. In the particular regime $\alpha =1/3$, these KPZ fluctuations suddenly vanish at a deterministic time.

References in corpus (6)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• KPZ equation limit of higher-spin exclusion processes
• Energy solutions of KPZ are unique
• ASEP(q,j) converges to the KPZ equation
• Scaling limits of weakly asymmetric interfaces
• On the scaling limits of weakly asymmetric bridges

Cited by in corpus (14)

• The KPZ Limit of ASEP with Boundary
• Cutoff phenomenon for the asymmetric simple exclusion process and the biased card shuffling
• Discretisation of regularity structures
• Energy solutions of KPZ are unique
• Non-equilibrium Fluctuations of Interacting Particle Systems
• KPZ equation limit of stochastic higher spin six vertex model
• ASEP(q,j) converges to the KPZ equation
• Open ASEP in the Weakly Asymmetric Regime
• Some recent progress in singular stochastic PDEs
• KPZ fluctuations in finite volume
• On the scaling limits of weakly asymmetric bridges
• Glauber dynamics of 2D Kac-Blume-Capel model and their stochastic PDE limits
• Large-scale limit of interface fluctuation models
• Scaling limit of a directed polymer among a Poisson field of independent walks