{"id":"openai-math/Spectral-convergence-for-critical-FK-Ising-planar-maps","pdf":"https://github.com/openai/math/blob/main/preprints/Spectral-convergence-for-critical-FK-Ising-planar-maps-October-5-2026/spectral-convergence-critical-fk-ising-planar-maps.pdf","url":"https://github.com/openai/math/tree/main/preprints/Spectral-convergence-for-critical-FK-Ising-planar-maps-October-5-2026","tags":["probability","random-planar-maps","liouville-quantum-gravity","spectral-geometry"],"score":0,"title":"Spectral convergence for critical FK–Ising planar maps","domain":"Probability and statistical mechanics","family":"211","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"Using the conformal and metric-measure companion results and the stated Brownian/Liouville quantum gravity inputs, we prove spectral convergence for critical spherical FK–Ising maps to Liouville Brownian motion on the ordinary unit-area $`\\sqrt3`$-quantum sphere. The discrete walk has total attempt rate one, uses every map edge including loops and multiplicities, and has the corner measure as its stationary law. Accelerating time by the number of map edges gives joint convergence of the metric-measure space, all ordered eigenvalues with multiplicities and padding, and the heat trace locally…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"The geometric phase diagram, diffusion, and spectra of random planar maps"}