  We consider a discrete one-dimensional random interface on the half-space
whose height at any positive point is defined as a sum of an independent random
noise and a function of the heights at its two closest neighbours. In 2022,
Adhikari and Chatterjee proved for the full-space model that assuming the
function is equivariant, symmetric, and at least six times differentiable in a
neighbourhood of zero, as the variance of the noise variables goes to zero, the
height function converges to the Cole-Hopf solution of the 1D KPZ equation
under a parabolic rescaling on full space. In this paper, we obtained the same
convergence result for such a random interface model with Robin boundary
conditions.
