The top level-line of the low-temperature Discrete Gaussian surface above a floor converges, after L^(1/3) rescaling, to a Ferrari-Spohn diffusion, and multiple top level-lines converge to independent copies.
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The limiting law of the Discrete Gaussian level lines
The top level-line of the low-temperature Discrete Gaussian surface above a floor converges, after L^(1/3) rescaling, to a Ferrari-Spohn diffusion, and multiple top level-lines converge to independent copies.