{"id":"openai-math/Brownian-continuum-random-tree-limits-of-finite-Fortuin-Kasteleyn-maps-above-four","pdf":"https://github.com/openai/math/blob/main/preprints/Brownian-continuum-random-tree-limits-of-finite-Fortuin-Kasteleyn-maps-above-four-September-24-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Brownian-continuum-random-tree-limits-of-finite-Fortuin-Kasteleyn-maps-above-four-September-24-2026","tags":["random-planar-maps","percolation","probability"],"score":0,"title":"Brownian continuum random tree limits of finite Fortuin–Kasteleyn maps above four","domain":"Probability and statistical mechanics","family":"211","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"The geometric phase diagram, diffusion, and spectra of random planar maps"}