相关论文: Convergence of the KPZ line ensemble
Many models of one-dimensional local random growth are expected to lie in the Kardar-Parisi-Zhang (KPZ) universality class. For such a model, the interface profile at advanced time may be viewed in scaled coordinates specified via…
These notes are based on a talk given at the 2018 Arizona School of Analysis and Mathematical Physics. We give a comprehensive introduction to the KPZ universality class, a conjectured class of stochastic process with local interactions…
The Airy line ensemble is a random collection of continuous ordered paths that plays an important role within random matrix theory and the Kardar-Parisi-Zhang universality class. The aim of this paper is to prove a universality property of…
In this paper, we establish the ergodicity of the Airy line ensemble. This shows that it is the only candidate for Conjecture 3.2 in [3], regarding the classification of ergodic line ensembles satisfying a certain Brownian Gibbs property…
For suitably discretized versions of the Kardar-Parisi-Zhang equation in one space dimension exact scaling functions are available, amongst them the stationary two-point function. We explain one central piece from the technology through…
We provide a comprehensive report on scale-invariant fluctuations of growing interfaces in liquid-crystal turbulence, for which we recently found evidence that they belong to the Kardar-Parisi-Zhang (KPZ) universality class for 1+1…
We prove the two dimensional KPZ equation with a logarithmically tuned nonlinearity and a small coupling constant, scales to the Edwards-Wilkinson equation with an effective variance.
We consider time correlation for KPZ growth in 1+1 dimensions in a neighborhood of a characteristics. We prove convergence of the covariance with droplet, flat and stationary initial profile. In particular, this provides a rigorous proof of…
This work considers the behavior of the height distributions of the equipotential lines in a region confined by two interfaces: a cathode with an irregular interface and a distant flat anode. Both boundaries, which are maintained at…
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…
Depinning of elastic systems advancing on disordered media can usually be described by the quenched Edwards-Wilkinson equation (qEW). However, additional ingredients such as anharmonicity and forces that can not be derived from a potential…
We develop a new probabilistic and geometric method to obtain several sharp results pertaining to the upper tail behavior of continuum Gibbs measures on infinite ensembles of random continuous curves, also known as line ensembles,…
Actions in the Airy line ensemble represent distances from an infinitely far object. We characterize the Airy sheet by S(x,.)=T^x(.,1), where T^x is the unique action in the Airy line ensemble satisfying a growth condition depending on x.…
We investigate the stationary-state fluctuations of a growing one-dimensional interface described by the KPZ dynamics with a noise featuring smooth spatial correlations of characteristic range $\xi$. We employ Non-perturbative Functional…
We prove that the Kipnis-Marchioro-Presutti (KMP) process converges to the Kardar-Parisi-Zhang (KPZ) equation, as time $t$ goes to infinity, in a properly scaled observation window shifted by $t^{3/4}$. Our proof is based on identifying the…
When a growing interface belonging to the KPZ universality class is tilted with average slope $m$, its average velocity increases in $\frac{\Lambda}{2}\,m^2$, where $\Lambda$ is related to the nonlinear coefficient $\lambda$ of the KPZ…
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)…
Correlation functions of the XXZ model in the massive and massless regimes are known to satisfy a system of linear equations. The main relations among them are the difference equations obtained from the qKZ equation by specializing the…
Gibbsian line ensembles are families of Brownian lines arising in many natural contexts such as the level curves of three dimensional Ising interfaces, the solid-on-solid model, multi-layered polynuclear growth etc. An important example is…
We propose a simple discrete model to study the nonequilibrium fluctuations of two locally coupled 1+1 dimensional systems (interfaces). Measuring numerically the tilt-dependent velocity we construct a set of stochastic continuum equations…