# An invariance principle for the 1D KPZ equation

@inproceedings{Adhikari2022AnIP, title={An invariance principle for the 1D KPZ equation}, author={Arka Adhikari and Sourav Chatterjee}, year={2022} }

A BSTRACT . Consider a discrete one-dimensional random surface whose height at a point grows as a function of the heights at neighboring points plus an independent random noise. Assuming that this function is equivariant under constant shifts, symmetric in its arguments, and at least six times continuously differentiable in a neighborhood of the origin, we show that as the variance of the noise goes to zero, any such process converges to the Cole–Hopf solution of the 1D KPZ equation under a…

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