Abstract We consider the stochastically forced Burgers equation with an emphasis on spatially rough driving noise. show that law of process at a fixed time t , conditioned no explosions, is absolutely continuous respect to stochastic heat obtained by removing nonlinearity from equation. This establishes form ellipticity in this infinite-dimensional setting. The results follow recasting Girsanov...

(1.4) hε(t, x) = ε 1/2h(ε−zt, ε−1x). We will be considering these models in equilibrium, in which case h(t, x)−h(t, 0) is a two-sided Brownian motion with variance ν−1σ2 for each t. There are many physical arguments for (1.3), none of which are good starting points for rigorous analysis, and which are really only convincing in the sense that they are very well backed up by numerical work. Perha...

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 probability 1-p. For any p>0, this system is in the Kardar-Parisi-Zhang (KPZ) universality class, but it presents a slow crossover from the Edwards-Wilkinson ...

We present a recently introduced real space renormalization group (RG) approach to the study of surface growth. The method permits us to obtain the properties of the KPZ strong coupling fixed point, which is not accessible to standard perturbative field theory approaches. Using this method, and with the aid of small Monte Carlo calculations for systems of linear size 2 and 4, we calculate the r...

This paper introduces a relative structural complexity measure for the characterization of disordered surfaces. Numerical solutions of 2d+1 KPZ equation and scanning force microscopy (SFM) patterns of porous silicon samples are analyzed using this methodology. The results and phenomenological interpretation indicate that the proposed measure is efficient for quantitatively characterize the stru...

– We present a new approach to the Kardar-Parisi-Zhang (KPZ) equation based on the non-perturbative renormalisation group (NPRG). The NPRG flow equations derived here, while embedding all the known analytical results, moreover allow to follow the strong-coupling fixed point describing the rough phase in all dimensions, and thus yield the qualitatively-robust complete phase diagram of the proble...

We consider a natural class of $\mathbf{R}^d$-valued one-dimensional stochastic PDEs driven by space-time white noise that is formally invariant under the action diffeomorphism group on $\mathbf{R}^d$. This contains in particular KPZ equation, multiplicative heat additive and rough Burgers-type equations. exhibit one-parameter family solution theories with following properties: - For all SPDEs ...

The Kardar-Parisi-Zhang equation (KPZ equation) is solved via Cole-Hopf transformation h=logu, where u the solution of multiplicative stochastic heat equation(SHE). In [CD20, CSZ20, G20], they consider two dimensional KPZ u? SHE with flat initial condition and noise which mollified in space on scale ? its strength weakened as ??=?ˆ 2? ?log?, prove that when ?ˆ?(0,1), 1 ??(logu??E[logu?]) conver...