The Gaussian free field in interlacing particle systems
arXiv:1109.4444
Abstract
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.
38 pages; version 2 has a rewritten introduction and more concise proofs