Triviality of the 2D stochastic Allen-Cahn equation

@article{Hairer2012TrivialityOT,
  title={Triviality of the 2D stochastic Allen-Cahn equation},
  author={Martin Hairer and Marc D. Ryser and Hendrik Weber},
  journal={Electronic Journal of Probability},
  year={2012},
  volume={17},
  pages={1-14}
}
We consider the stochastic Allen-Cahn equation driven by mollified space-time white noise. We show that, as the mollifier is removed, the solutions converge weakly to 0, independently of the initial condition. If the intensity of the noise simultaneously converges to 0 at a sufficiently fast rate, then the solutions converge to those of the deterministic equation. At the critical rate, the limiting solution is still deterministic, but it exhibits an additional damping term. 
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On the well-posedness of the stochastic Allen-Cahn equation in two dimensions

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