Suppose that $$\{u(t, x)\}_{t >0, x \in {\mathbb {R}}^d}$$ is the solution to a d-dimensional stochastic heat equation driven by Gaussian noise white in time and has spatially homogeneous covariance satisfies Dalang’s condition. The purpose of this paper establish quantitative central limit theorems for spatial averages form $$N^{-d} \int _{[0,N]^d} g(u(t,x))\, \mathrm {d}x$$ , as $$N\rightarro...

This Letter reports on how the interfaces in the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) class undergo, in the course of time, a transition from the flat, growing regime to the stationary one. Simulations of the polynuclear growth model and experiments on turbulent liquid crystal reveal universal functions of the KPZ class governing this transition, which connect the distribution and correl...

We present a simple criterion, only based on second moment assumptions, for the convergence of polynomial or Wiener chaos to Gaussian limit. exploit this criterion obtain new asymptotics partition functions two-dimensional directed polymers in sub-critical regime, including singular product between function and disorder. These results can also be applied KPZ Stochastic Heat Equation. As tool in...

The instanton solution for the forced Burgers equation is found. This solution describes the exponential tail of the probability distribution function of velocity differences in the region where shock waves are absent. The results agree with the one found recently by Polyakov, who used the operator product conjecture. If this conjecture is true, then our WKB asymptotics of the Wyld functional i...

An explicit Fredholm determinant formula is derived for the multipoint distribution of height function totally asymmetric simple exclusion process (TASEP) with arbitrary right-finite initial condition. The method by solving biorthogonal ensemble/non-intersecting path representation found [Sas05; BFPS07]. resulting kernel involves transition probabilities a random walk forced to hit curve define...

Abstract We study the two‐dimensional Anisotropic KPZ equation (AKPZ) formally given by where ξ is a space‐time white noise and λ strictly positive constant. While classical equation, whose nonlinearity , can be linearised via Cole‐Hopf transformation, this not case for AKPZ. prove that stationary solution to AKPZ (whose invariant measure Gaussian Free Field (GFF)) superdiffusive: its diffusion...