Family 226Probability and statistical mechanicsNo LeanNot yet digested
The double-dimer loop ensemble converges to CLE
Resolves the half-plane Temperleyan form of the double-dimer scaling-limit conjecture: the complete loop ensemble formed by two independent dimer coverings of the Temperleyan square lattice converges to nested CLE. Convergence matches every macroscopic loop as an unparametrized curve, upgrading convergence of loop observables to convergence of the loops themselves.
Manuscripts in this family · 1
The curve scaling limit of half-plane double dimers
Sep 23, 2026·paper.pdf
We prove that the complete double-dimer loop ensemble for the Temperleyan square lattice in the upper half-plane converges to nested CLE. The convergence holds along the full mesh limit and matches every macroscopic loop as an unparametrized curve. This resolves the half-plane Temperleyan form of the double-dimer CLE scaling-limit conjecture.