Rescaled Allen-Cahn solutions with supercritical short-range Gaussian initials converge to the heat equation started from white noise whose statistics incorporate the nonlinearity.
Random Initial Condi- tions for Semi-Linear PDEs
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Central limit theorem for the Allen-Cahn equation with supercritical random initial conditions
Rescaled Allen-Cahn solutions with supercritical short-range Gaussian initials converge to the heat equation started from white noise whose statistics incorporate the nonlinearity.