相关论文: The KPZ equation and the directed landscape

We show that the directed landscape is the unique coupling of the KPZ fixed point from all initial conditions satisfying three natural properties: independent increments, monotonicity, and shift commutativity. Equivalently, we show that the…

We define the log-gamma sheet and the log-gamma landscape in terms of the 2-parameter and 4-parameter free energy of the log-gamma polymer model and prove that they converge to the Airy sheet and the directed landscape, which are central…

Heat flows in 1+1 dimensional stochastic environment converge after scaling to the random geometry described by the directed landscape. In this first part, we show that the O'Connell-Yor polymer and the KPZ equation converge to the KPZ…

We show that under the 1:2:3 scaling, critically probing large space and time, the height function of finite range asymmetric exclusion processes and the KPZ equation converge to the KPZ fixed point, constructed earlier as a limit of the…

We provide a framework for proving convergence to the directed landscape, the central object in the Kardar-Parisi-Zhang universality class. For last passage models, we show that compact convergence to the Airy line ensemble implies…

Consider the restriction of the directed landscape $\mathcal L(x, s; y, t)$ to a set of the form $\{x_1, \dots, x_k\} \times \{s_0\} \times \mathbb R \times \{t_0\}$. We show that on any such set, the directed landscape is given by a last…

The results of Amir-Corwin-Quastel, Calabrese-Le Doussal-Rosso, Dotsenko, and Sasamoto-Spohn imply that the one-point distribution of the solution of the KPZ equation with the narrow wedge initial condition coincides with that for a…

We show that the increments of the KPZ fixed point started from arbitrary initial data are \emph{mutually} absolutely continuous with respect to Brownian motion with diffusion parameter $2$ on compacts, extending the one-sided Brownian…

We consider the directed mean curvature flow on the plane in a weak Gaussian random environment. We prove that, when started from a sufficiently flat initial condition, a rescaled and recentred solution converges to the Cole-Hopf solution…

We show that the directed landscape is a black noise in the sense of Tsirelson and Vershik. As a corollary, we show that for any microscopic system in which the height profile converges in law to the directed landscape, the driving noise is…

We prove that two half-space models in the KPZ universality class, exponential last-passage percolation and a family of Poisson-avoiding metrics generalizing colored TASEP, converge to a common scaling limit. This scaling limit is the…

We consider the system of one-sided reflected Brownian motions which is in variational duality with Brownian last passage percolation. We show that it has integrable transition probabilities, expressed in terms of Hermite polynomials and…

The KPZ fixed point is a 2d random field, conjectured to be the universal limiting fluctuation field for the height function of models in the KPZ universality class. Similarly, the periodic KPZ fixed point is a conjectured universal field…

We prove the upper-tail Large Deviation Principle (LDP) for the parabolic Airy process and characterize the limit shape of the directed landscape under the upper-tail conditioning. The LDP result answers Conjecture 10.1 in Das, Dauvergne,…

Our previous work on the one-dimensional KPZ equation with sharp wedge initial data is extended to the case of the joint height statistics at n spatial points for some common fixed time. Assuming a particular factorization, we compute an…

In this paper we study the KPZ line ensembles under the KPZ scaling. Based on their Gibbs property, we derive quantitative local fluctuation estimates for the scaled KPZ line ensembles. This allows us to show that the family of scaled KPZ…

We report on the first exact solution of the KPZ equation in one dimension, with an initial condition which physically corresponds to the motion of a macroscopically curved height profile. The solution provides a determinantal formula for…

We introduce a new concept of solution to the KPZ equation which is shown to extend the classical Cole-Hopf solution. This notion provides a factorisation of the Cole-Hopf solution map into a "universal" measurable map from the probability…

We introduce the notion of energy solutions of the KPZ equation. Under minimal assumptions, we prove that the density fluctuations of one-dimensional, weakly asymmetric, conservative particle systems with respect to the stationary states…

Temporal correlation for randomly growing interfaces in the KPZ universality class is a topic of recent interest. Most of the works so far have been concentrated on the zero temperature model of exponential last passage percolation, and…