Polynomial mixing for the complex Ginzburg--Landau equation perturbed by a random force at random times

TL;DR

This paper proves that the complex Ginzburg--Landau equation with random kicks has a unique stationary distribution and exhibits polynomial mixing, advancing understanding of its long-term statistical behavior.

Contribution

It establishes ergodicity and polynomial mixing for the complex Ginzburg--Landau equation with unbounded random perturbations at random times, a novel result in this context.

Findings

Unique stationary distribution proven for the perturbed equation

Demonstrates polynomial mixing property

Advances understanding of ergodic behavior under random kicks

Abstract

In this paper we study the problem of ergodicity for the complex Ginzburg--Landau equation perturbed by an unbounded random kick-force. Randomness is introduced both through the kicks and through the times between the kicks. We show that the Markov process associated with the equation in question possesses a unique stationary distribution and satisfies a property of polynomial mixing.