Eckmann, J. P.Hairer, Martin2024-09-172024-09-172024-09-112001-06-0110.1007/s0022001004242-s2.0-0035534238https://infoscience.epfl.ch/handle/20.500.14299/241220We consider the stochastic Ginzburg-Landau equation in a bounded domain. We assume the stochastic forcing acts only on high spatial frequencies. The low-lying frequencies are then only connected to this forcing through the non-linear (cubic) term of the Ginzburg-Landau equation. Under these assumptions, we show that the stochastic PDE has a unique invariant measure. The techniques of proof combine a controllability argument for the low-lying frequencies with an infinite dimensional version of the Malliavin calculus to show positivity and regularity of the invariant measure. This then implies the uniqueness of that measure.enfalsetext::journal::journal article::research article