The Gaussian free field in interlacing particle systems

Details The Gaussian free field in interlacing particle systems The Gaussian free field in interlacing particle systems

2011-09-20

arxiv.org/abs/1109.4444v1

Physics

Mathematical Physics

38 pages

Scientific paper

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, we examine a specific particle system that was previously studied and compute the corresponding Green's function.

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