Top level lines in the Discrete Gaussian model converge globally to deterministic shapes with Wulff corners; macroscopic h-level lines emerge discontinuously in a window of width at most L^{1/2+o(1)}.
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The limit shape and emergence of the Discrete Gaussian level lines
Top level lines in the Discrete Gaussian model converge globally to deterministic shapes with Wulff corners; macroscopic h-level lines emerge discontinuously in a window of width at most L^{1/2+o(1)}.