{"id":"openai-math/The-free-uniform-spanning-forest-is-a-factor-of-IID","pdf":"https://github.com/openai/math/blob/main/preprints/The-free-uniform-spanning-forest-is-a-factor-of-IID-September-25-2026/The-free-uniform-spanning-forest-is-a-factor-of-IID-September-25-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-free-uniform-spanning-forest-is-a-factor-of-IID-September-25-2026","tags":["probability","random-graphs","spanning-forests","unimodular-graphs"],"score":0,"title":"The free uniform spanning forest is a factor of IID","domain":"Probability and statistical mechanics","family":"231","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We prove that the free uniform spanning forest is a factor of IID on every infinite connected locally finite simple unweighted graph. One Borel rule works for all such graphs and uses no root, answering affirmatively the general factor question for unimodular random graphs. We also show that every translation-invariant strongly Rayleigh process indexed by a countable group is a factor of IID, including invariant determinantal processes with Hermitian positive-contraction kernels. This group-action conclusion requires no amenability.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"The free uniform spanning forest is a factor of IID"}