Related papers: Recent results on multiplicative noise

Reduced models for the (defocusing) nonlinear Schr\"odinger equation are developed. In particular, we develop reduced models that only involve the low-frequency modes given noisy observations of these modes. The ansatz of the reduced…

We review recent progress on the study of the Kardar-Parisi-Zhang (KPZ) equation in a periodic setting, which describes the random growth of an interface in a cylindrical geometry. The main results include central limit theorems for the…

A continuous approximation framework for non-linear stochastic as well as deterministic discrete maps is developed. For the stochastic map with uncorelated Gaussian noise, by successively applying the It\^o lemma, we obtain a Langevin type…

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…

When the drive which causes the level crossing in a qubit is slow, the probability, P_{LZ}, of the Landau-Zener transition is close to 1. We show that in this regime, which is most promising for applications, the noise due to the coupling…

We study in this article the stochastic Zakharov-Kuznetsov equation driven by a multiplicative noise. We establish, in space dimensions two and three the global existence of martingale solutions, and in space dimension two the global…

The model introduced by Van den Broeck, Parrondo and Toral [Phys. Rev. Lett.73, 3395 (1994)] -- leading to a second-order-like noise-induced nonequilibrium phase transition which shows reentrance as a function of the (multiplicative) noise…

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,…

Recently, Newman and Swift[T. J. Newman and M. R. Swift, Phys. Rev. Lett. {\bf 79}, 2261 (1997)] made an interesting suggestion that the strong-coupling exponents of the Kardar-Parisi-Zhang (KPZ) equation may not be universal, but rather…

A time-discrete approach avoids the assumption of an 'integration sense'. New path increments (in a short time step) are complete in the order of that step, and not Gaussian distributed when the noise is multiplicative; this eliminates an…

We consider the 2D incompressible Navier-Stokes equations driven by mildly degenerate noise that acts only on finitely many low Fourier modes, a setting that models large-scale stirring. For this system, we prove that the top Lyapunov…

We propose a general Langevin equation describing the universal properties of synchronization transitions in extended systems. By means of theoretical arguments and numerical simulations we show that the proposed equation exhibits,…

A recent paper of Melbourne & Stuart, A note on diffusion limits of chaotic skew product flows, Nonlinearity 24 (2011) 1361-1367, gives a rigorous proof of convergence of a fast-slow deterministic system to a stochastic differential…

The strong-coupling regime of Kardar-Parisi-Zhang surface growth driven by short-ranged noise has an upper critical dimension d_> less or equal to four (where the dynamic exponent z takes the value z (d_>) = 2). To derive this, we use the…

The stochastic PDE known as the Kardar-Parisi-Zhang equation (KPZ) has been proposed as a model for a randomly growing interface. This equation can be reformulated as a stochastic Burgers equation. We study a stochastic KdV-Burgers equation…

{\em NOTE: This paper presented the first attempt to tackle the Kardar-Parisi-Zhang (KPZ) equation using non-perturbative renormalisation group (NPRG) methods. It exploited the most natural and frequently used approximation scheme within…

The one-dimensional Kardar-Parisi-Zhang (KPZ) equation is becoming an overarching paradigm for the scaling of nonequilibrium, spatially extended, classical and quantum systems with strong correlations. Recent analytical solutions have…

We provide a simple framework for the study of parametric (multiplicative) noise, making use of scale parameters. We show that for a large class of stochastic differential equations increasing the multiplicative noise intensity surprisingly…

A Langevin equation with multiplicative noise is an equation schematically of the form dq/dt = -F(q) + e(q) xi, where e(q) xi is Gaussian white noise whose amplitude e(q) depends on q itself. Such equations are ambiguous, and depend on the…

We examine the effects of pure additive noise on spatially extended systems with quadratic nonlinearities. We develop a general multiscale theory for such systems and apply it to the Kuramoto-Sivashinsky equation as a case study. We first…