We show that if an interlacing particle system in a two-dimensional lattice is a determinantal point process, and the correlation kernel can be expressed as a double integral with certain technical assumptions, then the moments of the fluctuations of the height function converge to that of the Gaussian free field. In particular, this shows that a previously studied random surface growth model with a reflecting wall has Gaussian free field fluctuations.
"The Gaussian free field in interlacing particle systems." Electron. J. Probab. 19 1 - 31, 2014. https://doi.org/10.1214/EJP.v19-3732