We examine numerically the zero-temperature (2+1)-dimensional directed polymer in a random medium, along with several of its brethren via the Kardar-Parisi-Zhang (KPZ) equation. Using finite-size and KPZ scaling Ansätze, we extract the universal distributions controlling fluctuation phenomena in this canonical model of nonequilibrium statistical mechanics. Specifically, we study point-point, po...

To this day, computer models for stromatolite formation have made substantial use of the Kardar-Parisi-Zhang (KPZ) equation. Oddly enough, these studies yielded mutually exclusive conclusions about the biotic or abiotic origin of such structures. We show in this paper that, at our current state of knowledge, a purely biotic origin for stromatolites can neither be proved nor disproved by means o...

The stochastic nonlinear partial differential equation known as the Kardar-Parisi-Zhang (KPZ) equation is a highly successful phenomenological mesoscopic model of surface and interface growth processes. Its suitability for analytical work, its explicit symmetries and its prediction of an exact dynamic scaling relation for a one-dimensional substratum led people to adopt it as a 'standard' model...

The effects of spatially correlated noise on a phenomenological equation equivalent to a non-local version of the Kardar-Parisi-Zhang (KPZ) equation are studied via the dynamic renormalization group (DRG) techniques. The correlated noise coupled with the long ranged nature of interactions prove the existence of different phases in different regimes, giving rise to a range of roughness exponents...

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 this equation. Bertini, Cancrini and Giacomin [2, 3] have proposed a notion of a solution through a limiting procedure and a certain renormalization of the ...

We consider a discrete bridge from (0, 0) to (2N, 0) evolving according to the corner growth dynamics, where the jump rates are subject to an upward asymmetry of order N with α > 0. We provide a classification of the static and dynamic behaviour of this model according to the value of the parameter α. Our main results concern the hydrodynamic limit and the fluctuations of the bridge. For α < 1,...

We apply a number of schemes which variationally improve perturbation theory for the Kardar-Parisi-Zhang equation in order to extract estimates for the dynamic exponent z. The results for the various schemes show the same broad features, giving closer agreement with numerical simulations in low dimensions than self-consistent methods. They do, however, continue to predict that z = 2 in some cri...

We consider the $(1+1)$-dimensional stochastic heat equation (SHE) with multiplicative white noise and Cole-Hopf solution of Kardar-Parisi-Zhang (KPZ) equation. show an exact way computing Lyapunov exponents SHE for a large class initial data which includes any bounded deterministic positive stationary data. As consequence, we derive formulas upper tail deviation rate functions KPZ general

In order to perform numerical simulations of the Kardar-Parisi-Zhang (KPZ) equation, in any dimensionality, a spatial discretization scheme must be prescribed. The known fact that the KPZ equation can be obtained as a result of a Hopf-Cole transformation applied to a diffusion equation (with multiplicative noise) is shown here to strongly restrict the arbitrariness in the choice of spatial disc...