We consider the KPZ equation in $1$ spatial dimension with noise that is rougher than white by an exponent γ>1/4. Under a weak coupling limit, formally removing the nonlinearity from the equation, we show using regularity structures that the renormalised solutions converge to a Gaussian limit that is different from the solution of the linear part of the equation. The regime of this effect has a nontrivial overlap with the subcritical regime γ<1/2.
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Gerencsér et al. (2024) studied this question.
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