相关论文: Temporal increments of the KPZ equation with gener…

The early time regime of the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimension, starting from a Brownian initial condition with a drift $w$, is studied using the exact Fredholm determinant representation. For large drift we recover the…

The fractional Brownian motion can be considered as a Gaussian field indexed by $(t,H)\in {\mathbb{R}_{+}\times (0,1)}$, where $H$ is the Hurst parameter. On compact time intervals, it is known to be almost surely jointly H\"older…

We consider the asymptotic behavior of the KPZ fixed point $\{\mathsf H(x,t)\}_{x\in\mathbb R, t>0}$ conditioned on $\mathsf H(0,T)=L$ as $L$ goes to infinity. The main result is a conditional limit theorem for the fluctuations of $\mathsf…

The short time behavior of the 1+1 dimensional KPZ growth equation with a flat initial condition is obtained from the exact expressions of the moments of the partition function of a directed polymer with one endpoint free and the other…

Let $Z = (Z_t)_{t \geq 0}$ be the Rosenblatt process with Hurst index $H \in (1/2, 1)$. We prove joint continuity for the local time of $Z$, and establish H\"older conditions for the local time. These results are then used to study the…

We show that the spatial increments of the KPZ fixed point starting from arbitrary initial data, exhibit strong quantitative comparison against rate two Brownian motion on compacts. The above estimates are uniform in the initial data…

We consider the stochastic heat equation $\partial_tZ= \partial_x^2 Z - Z \dot W$ on the real line, where $\dot W$ is space-time white noise. $h(t,x)=-\log Z(t,x)$ is interpreted as a solution of the KPZ equation, and $u(t,x)=\partial_x…

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…

We study quantitative large-time averages for Hamilton--Jacobi equations in a dynamic random environment that is stationary ergodic and has unit-range dependence in time. Our motivation comes from stochastic growth models related to the…

We study the long-time regime of the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimensions for the Brownian and droplet initial conditions and present a simple derivation of the tail of the large deviations of the height on the negative…

While the 1-point height distributions (HDs) and 2-point covariances of $(2+1)$ KPZ systems have been investigated in several recent works for flat and spherical geometries, for the cylindrical one the HD was analyzed for few models and…

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…

We construct a family of stochastic growth models in 2+1 dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield 1+1 dimensional growth models in the KPZ class and random tiling models. We show…

We present a systematic short time expansion for the generating function of the one point height probability distribution for the KPZ equation with droplet initial condition, which goes much beyond previous studies. The expansion is checked…

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 study the short-time behavior of the probability distribution $\mathcal{P}(H,t)$ of the surface height $h(x=0,t)=H$ in the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimension. The process starts from a stationary interface: $h(x,t=0)$…

We study the Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with a noise variance $c(t)$ depending on time. We find that for $c(t)\propto t^{-\alpha}$ there is a transition at $\alpha=1/2$. When $\alpha>1/2$, the solution…

The statistics of the average height fluctuation of the one-dimensional Kardar-Parisi-Zhang(KPZ)-type surface is investigated. Guided by the idea of local stationarity, we derive the scaling form of the characteristic function in the…

The focus of this work is the numerical approximation of time-dependent partial differential equations associated to initial-boundary value problems. This master dissertation is mostly concerned with the actual computation of the solution…

We consider a large class of $1+1$-dimensional continuous interface growth models and we show that, in both the weakly asymmetric and the intermediate disorder regimes, these models converge to Hopf-Cole solutions to the KPZ equation.