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The Gaussian free field in interlacing particle systems

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arxiv 1109.4444 v2 pith:57XI6VMY submitted 2011-09-20 math-ph math.MPmath.PR

Jeffrey Kuan This is my paper · ORCID
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keywords fieldfreegaussianfluctuationsinterlacingparticleassumptionscertain
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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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  1. Gaussian Free Field and Discrete Gaussians in Periodic Dimer Models

    math.PR 2025-02 conditional novelty 7.0 of 10

    Periodic Aztec diamond height fluctuations are shown to decompose into a Gaussian free field plus a discrete-Gaussian random harmonic component.

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