This note shows chaos onset on the scale of 1/t in stochastic equations, suggesting implications for solution behavior.
In this note, we consider the stochastic heat and Schrödinger equations, and show that, at time t, the onset of the chaos occurs on the scale of 1/t, and the Fourier spectrum of the solution is asymptotically Gaussian after centering and rescaling.
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Gu et al. (2025) studied this question.
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