The Gaussian free field in interlacing particle systems

Jeffrey Kuan (Harvard University)

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.

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Pages: 1-31

Publication Date: August 15, 2014

DOI: 10.1214/EJP.v19-3732

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