ALE scaling-limit conjecture for boundary-touching curves in free boundary dimers
ALE scaling-limit conjecture for boundary-touching curves in free boundary dimers
For any , 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 . 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.
Sources & referencesView supporting material
Primary source
Nathanael Berestycki, Marcin Lis and Wei Qian, “Free boundary dimers: random walk representation and scaling limit”, arXiv:2102.12873 (2021).
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.