June 12, 2024Open Access

Weak coupling limit of KPZ with rougher than white noise

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Abstract

We consider the KPZ equation in 1 spatial dimension with noise that is rougher than white by an exponent >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 <1/2.

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Gerencsér et al. (Wed,) studied this question.

synapsesocial.com/papers/68e651cbb6db6435875e2612 https://doi.org/https://doi.org/10.48550/arxiv.2406.08364

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