Spatial averages of the critical SHE with Riesz-2 noise are Gaussian at times much smaller than R^2, non-Gaussian at time proportional to R^2, and go extinct at times much larger than R^2.
A Central Limit Theorem for the stochastic wave equation with fractional noise
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Time-dependent averages of a critical long-range stochastic heat equation
Spatial averages of the critical SHE with Riesz-2 noise are Gaussian at times much smaller than R^2, non-Gaussian at time proportional to R^2, and go extinct at times much larger than R^2.