Noise sensitivity for stochastic heat and Schrödinger equations
Bulletin Polish Acad. Sci. Math.
MSC: Primary 35R60; Secondary 60H15, 35Q82
DOI: 10.4064/ba250422-15-9
Published online: 6 October 2025
Abstract
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.
