{"id":"openai-math/Metric-measure-limits-of-subcritical-FK-and-spanning-tree-planar-maps","pdf":"https://github.com/openai/math/blob/main/preprints/Metric-measure-limits-of-subcritical-FK-and-spanning-tree-planar-maps-September-24-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Metric-measure-limits-of-subcritical-FK-and-spanning-tree-planar-maps-September-24-2026","tags":["liouville-quantum-gravity","random-planar-maps","percolation","scaling-limits"],"score":0,"title":"Metric-measure limits of subcritical FK and spanning-tree planar maps","domain":"Probability and statistical mechanics","family":"211","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We resolve the finite spherical cases of Gwynne and Miller's graph-metric conjecture for critical Fortuin–Kasteleyn maps at each fixed $`q\\in(0,4)`$ and for uniform spanning-tree-decorated maps. After deterministic rescaling of graph distances, these maps, equipped with the vertex probability measure proportional to degree, converge in Gromov–Hausdorff–Prokhorov law to their ordinary unit-area Liouville quantum gravity spheres. Distances use every primal edge, and convergence holds through all positive integer edge counts.","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"}