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On the rigidity of sloped height functions in $d\ge 3$ and non-crossing surfaces
We consider integer-valued $\nablaϕ$ height functions, with general convex interactions, placed on a slope. Sheffield (2003) conjectured that for all slopes, such height functions are localized in dimensions $d\ge3$, in the sense of having tight fluctuations in finite volume, and admitting infinite-
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