Related papers: The KPZ Limit of ASEP with Boundary

We consider ASEP on a bounded interval and on a half line with sources and sinks. On the full line, Bertini and Giacomin proved convergence under weakly asymmetric scaling of the height function to the solution of the KPZ equation. We prove…

We consider generalizations of open ASEP in the interval and half-space, where the speed of the reservoir dynamics can depend on the local particle configuration. We show that their height functions have a continuum limit given by the open…

We consider a discrete one-dimensional random interface on the half-space whose height at any positive point is composed of a function of the heights at its two closest neighbours and an independent random noise background. In [AC24],…

We consider the ASEP and the stochastic six vertex model started with step initial data. After a long time, $T$, it is known that the one-point height function fluctuations for these systems are of order $T^{1/3}$. We prove the KPZ…

This paper has two main goals. The first is universality of the KPZ equation for fluctuations of dynamic interfaces associated to interacting particle systems in the presence of open boundary. We consider generalizations on the open-ASEP…

We consider the asymmetric simple exclusion process (ASEP) on the positive integers with an open boundary condition. We show that, when starting devoid of particles and for a certain boundary condition, the height function at the origin…

For each $\alpha \in \mathbb{R}$, $t \geq 1$, we show that there exists a unique $\mathbb{N}$-indexed line ensemble of random continuous curves $\mathbb{R}_{\le 0} \to \mathbb{R}$ with the following properties: (1) The top curve is…

We study fluctuations of the current at the boundary for the half space asymmetric simple exclusion process (ASEP) and the height function of the half space six vertex model at the boundary at large times. We establish a phase transition…

We continue the investigation of limit fluctuations of stationary measures of the asymmetric simple exclusion processes with open boundaries (open ASEP), complementing the recent result by Bryc et al. (2023). It was shown therein that in…

We study the half-space KPZ equation with a Neumann boundary condition, starting from stationary Brownian initial data. We derive a variance identity that links the fluctuations of the height function to the transversal fluctuations of a…

We study ASEP in a spatially inhomogeneous environment on a torus $ \mathbb{T}^{(N)} = \mathbb{Z}/N\mathbb{Z} $ of $ N $ sites. A given inhomogeneity $ \widetilde{a}(x) \in (0,\infty) $, $x \in \mathbb{T} $, perturbs the overall asymmetric…

We consider the stochastic six-vertex (S6V) model and asymmetric simple exclusion process (ASEP) under general initial conditions which are bounded below lines of arbitrary slope at $\pm\infty$. We show under Kardar-Parisi-Zhang (KPZ)…

We establish the first tight bound on the lower tail probability of the half-space KPZ equation with Neumann boundary parameter $A = -1/2$ and narrow-wedge initial data. When the tail depth is of order $T^{2/3}$, the lower bound…

We demonstrate that Liggett's condition can be relaxed without disrupting the convergence of open ASEP stationary measures to the open KPZ stationary measure. This is equivalent to demonstrating that, under weak asymmetry scaling and…

We prove the height functions for a class of non-integrable and non-stationary particle systems converge to the KPZ equation, thereby making progress on the universality of the KPZ equation. The models herein are ASEP [4] with a mesoscopic…

We consider the half-line stochastic heat equation (SHE) with Robin boundary parameter $A = -\frac{1}{2}$. Under narrow wedge initial condition, we compute every positive (including non-integer) Lyapunov exponents of the half-line SHE. As a…

We study spaces of modelled distributions with singular behaviour near the boundary of a domain that, in the context of the theory of regularity structures, allow one to give robust solution theories for singular stochastic PDEs with…

Current fluctuations for the one-dimensional totally asymmetric exclusion process (TASEP) connected to reservoirs of particles, and their large scale limit to the KPZ fixed point in finite volume, are studied using exact methods. Focusing…

We consider the KPZ equation in one space dimension driven by a stationary centred space-time random field, which is sufficiently integrable and mixing, but not necessarily Gaussian. We show that, in the weakly asymmetric regime, the…

We consider the colored asymmetric simple exclusion process (ASEP) and stochastic six vertex (S6V) model with fully packed initial conditions; the states of these models can be encoded by 2-parameter height functions. We show under…