相关论文: Simple derivation of the $(- \lambda H)^{5/2}$ tai…

We consider the relaxation (noise-free) statistics of the one-point height $H=h(x=0,t)$ where $h(x,t)$ is the evolving height of a one-dimensional Kardar-Parisi-Zhang (KPZ) interface, starting from a Brownian (random) initial condition. We…

We obtain the first exact solution for the stationary one-dimensional Kardar-Parisi-Zhang equation. A formula for the distribution of the height is given in terms of a Fredholm determinant, which is valid for any finite time $t$. The…

We provide the first tight bounds on the lower tail probability of the one point distribution of the KPZ equation with narrow wedge initial data. Our bounds hold for all sufficiently large times $T$ and demonstrates a crossover between…

We consider an infinite interface in $d>2$ dimensions, governed by the Kardar-Parisi-Zhang (KPZ) equation with a weak Gaussian noise which is delta-correlated in time and has short-range spatial correlations. We study the probability…

We consider the Kardar-Parisi-Zhang (KPZ) fixed point $\mathrm{H}(x,\tau)$ with the narrow-wedge initial condition and investigate the distribution of $\mathrm{H}(x,\tau)$ conditioned on a large height at an earlier space-time point…

The Kardar-Parisi-Zhang (KPZ) equation is a stochastic partial differential equation which is derived from various microscopic models, and to establish a robust way to derive the KPZ equation is a fundamental problem both in mathematics and…

Recent theoretical studies have gradually deepened our understanding of the one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) universality class even in the large deviation regime, but numerical methods for studying KPZ large deviations remain…

Consider the solution $\mathcal{Z}(t,x)$ of the one-dimensional stochastic heat equation, with a multiplicative spacetime white noise, and with the delta initial data $\mathcal{Z}(0,x) = \delta(x)$. For any real $p>0$, we obtained detailed…

We simulated a growth model in 1+1 dimensions in which particles are aggregated according to the rules of ballistic deposition with probability p or according to the rules of random deposition with surface relaxation (Family model) with…

Consider a stochastic interface $h(x,t)$, described by the $1+1$ Kardar-Parisi-Zhang (KPZ) equation on the half-line $x\geq 0$. The interface is initially flat, $h(x,t=0)=0$, and driven by a Neumann boundary condition $\partial_x…

In this paper, we study large time large deviations for the height function $\mathfrak{h}(x,t)$ of the $q$-deformed polynuclear growth introduced in ABW22 [arXiv:2108.06018]. We show that the upper-tail deviations have speed $t$ and derive…

We obtain several exact results for universal distributions involving the maximum of the Airy$_2$ process minus a parabola and plus a Brownian motion, with applications to the 1D Kardar-Parisi-Zhang (KPZ) stochastic growth universality…

We establish the Freidlin--Wentzell Large Deviation Principle (LDP) for the Stochastic Heat Equation with multiplicative noise in one spatial dimension. That is, we introduce a small parameter $ \sqrt{\varepsilon} $ to the noise, and…

The Kardar-Parisi-Zhang (KPZ) fixed point is a Markov process that is conjectured to be at the core of the KPZ universality class. In this article we study two aspects the KPZ fixed point that share the same Brownian limiting behaviour: the…

Growth of interfaces during vapor deposition is analyzed on a discrete lattice. It leads to finding distribution of local heights, measurable for any lattice model. Invariance in the change of this distribution in time is used to determine…

A novel algorithm is envisaged to extract the coupling parameters of the Kardar-Parisi-Zhang (KPZ) equation from experimental data. The method hinges on the Fokker-Planck equation combined with a classical least-square error procedure. It…

An analytical derivation of the probability density function (PDF) tail describing the strongly correlated interface growth governed by the nonlinear Kardar-Parisi-Zhang equation is provided. The PDF tail exactly coincides with a…

We study the short-time distribution $\mathcal{P}\left(H,L,t\right)$ of the two-point two-time height difference $H=h(L,t)-h(0,0)$ of a stationary Kardar-Parisi-Zhang (KPZ) interface in 1+1 dimension. Employing the optimal-fluctuation…

We consider the KPZ equation in one space dimension with narrow wedge initial condition, $h(x,t=0)=- |x|/\delta$, $\delta\ll 1$. Based on previous results for the weakly asymmetric simple exclusion process with step initial conditions, we…

We study in the present article the Kardar-Parisi-Zhang (KPZ) equation $$ \partial_t h(t,x)=\nu\Delta h(t,x)+\lambda |\nabla h(t,x)|^2 +\sqrt{D}\, \eta(t,x), \qquad (t,x)\in\mathbb{R}_+\times\mathbb{R}^d $$ in $d\ge 3$ dimensions in the…