ALE scaling-limit conjecture for boundary-touching curves in free boundary dimers

For any z>0z>0, superimpose two independent free boundary dimer models in the upper half-plane, and consider the resulting collection of boundary-touching curves. Free-boundary dimer ALE conjecture. In the scaling limit, this collection converges to the Arc Loop Ensemble, denoted by ALE\mathrm{ALE}. The Arc Loop Ensemble is the law identified with level lines of a Gaussian free field with Neumann boundary conditions; the source gives no resolution of this conjecture.

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Primary source

Nathanael Berestycki, Marcin Lis and Wei Qian, “Free boundary dimers: random walk representation and scaling limit”, arXiv:2102.12873 (2021).

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