Critical bond and site percolation on the cubic lattice
Source: github.com/openai/math/tree/main/preprints/Critical-bond-an…
We prove that nearest-neighbor Bernoulli bond and site percolation on ℤ 3 have no infinite cluster at their respective critical parameters. The proof combines a finite connection inequality for independent hyperedges with a finite-scale extension estimate and an adaptive exploration.
Comments and reviews
No comments yet.
Discussed elsewhere
API
curl /api/v1/records/openai-math/Critical-bond-and-site-percolation-on-the-cubic-lattice
curl -X POST /api/v1/records/openai-math/Critical-bond-and-site-percolation-on-the-cubic-lattice/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/openai-math/Critical-bond-and-site-percolation-on-the-cubic-lattice/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'
What I write about the day after the most earth-shattering event in the history of mathematicshaggstrom.substack.comOlle HäggströmOct 7, 2026
Do I explain the significance of the solutions to problems in percolation theory (such as this one , and this one , and this one , and this one , and this one ) that I used to put so much effort into solving (but of course failing) back in the 90s and early 00s? Do I attempt a bit of ego-boost by…