Related papers: Ergodicity for the stochastic Complex Ginzburg-Lan…
Averaging principle is an effective method for investigating dynamical systems with highly oscillating components. In this paper, we study three types of averaging principle for stochastic complex Ginzburg-Landau equations. Firstly, we…
We analyze the long-time behavior of numerical schemes for a class of monotone stochastic partial differential equations (SPDEs) driven by multiplicative noise. By deriving several time-independent a priori estimates for the numerical…
We establish general quantitative conditions for stochastic evolution equations with locally monotone drift and degenerate additive Wiener noise in variational formulation resulting in the existence of a unique invariant probability measure…
We prove stochastic stability of chaotic maps for a general class of Markov random perturbations (including singular ones) satisfying some kind of mixing conditions. One of the consequences of this statement is the proof of Ulam's…
We provide a coupling proof of Doob's theorem which says that the transition probabilities of a regular Markov process which has an invariant probability measure $\mu$ converge to $\mu$ in the total variation distance. In addition we show…
We present results from a comprehensive analytical and numerical study of nonequilibrium dynamics in the 2-dimensional complex Ginzburg-Landau (CGL) equation. In particular, we use spiral defects to characterize the domain growth law and…
We consider a finite dimensional approximation of the stochastic nonlinear Schr\"odinger equation driven by multiplicative noise, which is derived by applying a symplectic method to the original equation in spatial direction. Both the…
We provide a simple hypocoercivity analysis for the effective Mori-Zwanzig equation governing the time evolution of noise-averaged observables in a stochastic dynamical system. Under the hypocoercivity framework mainly developed by…
The complex Ginzburg-Landau equation with additive noise is a stochastic partial differential equation that describes a remarkably wide range of physical systems which include coupled non-linear oscillators subject to external noise near a…
We construct a Ginsburg Landau (GL) theory to study the phases of liquid, solid, superfluid, especially a possible supersolid and phase transitions among these phases in a unified framework. In this GL, we put the two competing orders…
Stochastic Gradient Langevin Dynamics (SGLD) is a popular variant of Stochastic Gradient Descent, where properly scaled isotropic Gaussian noise is added to an unbiased estimate of the gradient at each iteration. This modest change allows…
We study the statistics and characteristics of rare intense events in two types of two dimensional Complex Ginzburg-Landau (CGL) equation based models. Our numerical simulations show finite amplitude collapse-like solutions which approach…
We study ergodic properties of a family of traffic maps acting in the space of bi-infinite sequences of real numbers. The corresponding dynamics mimics the motion of vehicles in a simple traffic flow, which explains the name. Using…
We study the asymptotic behavior of solutions to stochastic evolution equations with monotone drift and multiplicative Poisson noise in the variational setting, thus covering a large class of (fully) nonlinear partial differential equations…
This work aims to investigate the existence of ergodic invariant measures and its uniqueness, associated with obstacle problems governed by a T-monotone operator defined on Sobolev spaces and driven by a multiplicative noise in a bounded…
We develop a theory of ergodicity for a class of random dynamical systems where the driving noise is not white. The two main tools of our analysis are the strong Feller property and topological irreducibility, introduced in this work for a…
This paper continues the study of the Gregory-Laflamme instability of black strings, or more precisely of the order of the transition, being either first or second order, and the critical dimension which separates the two cases. First, we…
We study the limiting behavior of the two-dimensional singular stochastic stochastic cubic nonlinear complex Ginzburg-Landau with Gibbs measure initial data. We show that in the appropriate small viscosity and small noise regimes, the…
We employ the perturbative field-theoretic renormalization group method to investigate the universal critical behavior near the continuous non-equilibrium phase transition in the complex Ginzburg-Landau equation with additive white noise.…
We provide sufficient conditions for the uniqueness of an invariant measure of a Markov process as well as for the weak convergence of transition probabilities to the invariant measure. Our conditions are formulated in terms of generalized…