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Brownian continuum random tree limits of finite Fortuin–Kasteleyn maps above four

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OpenAI Mathopenai-math/Brownian-continuum-random-tree-limits-of-finite-Fortuin-Kasteleyn-maps-above-fourSep 24, 2026math.PRAI-generatedscore 0

We prove the finite-volume continuum-random-tree prediction for critical Fortuin–Kasteleyn planar maps at every fixed q > 4. After rescaling graph distances by a constant times n −1/2 , an n -edge map with normalized degree measure converges to the Brownian continuum random tree in the Gromov–Hausdorff–Prokhorov topology. The convergence holds through all positive integer sizes.

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