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The Gaussian free field in interlacing particle systems
Published 20 Sep 2011 in math-ph, math.MP, and math.PR | (1109.4444v2)
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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