PDE and mathematical physics · Oct 6, 2026

Random-cluster interfaces: critical, disordered, thermal, and natural-time scaling

Proves chordal SLEκ limits for critical square-lattice random-cluster interfaces for

0\lt q\le4

, with

\kappa=4\pi/\arccos(-\sqrt q/2)

: bounded Jordan domains are allowed for q ≥ 1, and smooth Jordan domains for q < 1, under the stated marked-boundary approximations. For

1\le q\le4

, complete nested plane loops converge to CLEκ.

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