Related papers: Large deviations for the KPZ equation from the KP …
Kardar-Parisi-Zhang (KPZ) equation is a quasilinear stochastic partial differential equation(SPDE) driven by a space-time white noise. In recent years there have been several works directed towards giving a rigorous meaning to a solution of…
We study the atypically large deviations of the height $H \sim {{\cal O}}(t)$ at the origin at late times in $1+1$-dimensional growth models belonging to the Kardar-Parisi-Zhang (KPZ) universality class. We present exact results for the…
We study the Kardar-Parisi-Zhang equation on the half-line $x \geqslant 0$ with Neumann type boundary condition. Stationary measures of the KPZ dynamics were characterized in recent work: they depend on two parameters, the boundary…
We consider the early time regime of the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimensions in curved (or droplet) geometry. We show that for short time $t$, the probability distribution $P(H,t)$ of the height $H$ at a given point $x$…
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…
The Kardar-Parisi-Zhang (KPZ) fixed point is a Markov process, recently introduced by Matetski, Quastel, Remenik (arXiv:1701.00018), that describes the limit fluctuations of the height function associated to the totally asymmetric simple…
We study atypically large fluctuations of height $H$ in the 1+1-dimensional Kardar-Parisi-Zhang (KPZ) equation at long times $t$, when starting from a "droplet" initial condition. We derive exact large deviation function of height for…
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 present a variational formulation for the Kardar-Parisi-Zhang (KPZ) equation that leads to a thermodynamic-like potential for the KPZ as well as for other related kinetic equations. For the KPZ case, with the knowledge of such a…
We present a variational formulation for the Kardar-Parisi-Zhang (KPZ) equation that leads to a thermodynamic-like potential for the KPZ as well as for other related kinetic equations. For the KPZ case, with the knowledge of such a…
A master equation for the Kardar-Parisi-Zhang (KPZ) equation in 2+1 dimensions is developed. In the fully nonlinear regime we derive the finite time scale of the singularity formation in terms of the characteristics of forcing. The exact…
In a recent contribution, Dotsenko establishes a Fredholm determinant formula for the two-point distribution of the KPZ equation in the long time limit and starting from narrow wedge initial conditions. We establish that his expression is…
The Kardar-Parisi-Zhang (KPZ) equation on the real line is well-known to admit Brownian motion with a linear drift as a stationary distribution (modulo additive constants). We show that these solutions are attractive, a result known as a…
In this paper we obtain local in time existence and (suitable) uniqueness and continuous dependence for the KP-I equation for small data in the intersection of the energy space and a natural weighted $L^{2}$ space.
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…
We prove large time asymptotics for solutions of the KP I equation with small initial data. Our assumptions on the initial data rule out lump solutions but give a precise description of the radiation field at large times. Our analysis uses…
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 consider the Kardar-Parisi-Zhang equation on the interval $[0,L]$ with Neumann type boundary conditions and boundary parameters $u,v$. We show that the $k$-th order cumulant of the height behaves as $c_k(L,u,v)\, t$ in the large time…
The Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimension dynamically develops sharply connected valley structures within which the height derivative {\it is not} continuous. There are two different regimes before and after creation of the…
Here we propose the Donsker-Varadhan-type compactness conditions and prove the joint large deviation principle for the empirical measure and empirical flow of Markov renewal processes (semi-Markov processes) with a countable state space,…