Science
Mathematicians at ETH Zurich solve decades-old supercritical sharpness conjecture
A five-person research team established a proof describing phase transitions on infinite transitive graphs within percolation theory.
The short version
- Five mathematicians at ETH Zurich developed a proof solving the supercritical half of the sharpness conjecture for all infinite transitive graphs.
- The proof resolves a long-standing open question regarding the speed at which percolation networks transition into large, connected fluid networks above a critical probability threshold.
- The team utilized a probability technique known as sprinkling alongside an analysis of isolated pool shorelines to demonstrate that large isolated pools become highly unlikely above critical thresholds.
Key facts
- Researchers Sahar Diskin, Philip Easo, Ritvik Ramanan Radhakrishnan, Benny Sudakov, and Vincent Tassion completed the percolation proof at ETH Zurich around December 2025.[Hacker News]
- The proof completes the supercritical half of the sharpness conjecture for all infinite transitive graphs, addressing how quickly percolation networks flood.[Hacker News]
- The subcritical half of the sharpness conjecture was previously solved in 2007 by Tonći Antunović and Ivan Veselić.[Hacker News]
- To achieve the proof, the researchers used a probability technique called sprinkling and analyzed the shorelines of isolated fluid pools to demonstrate that large isolated pools are unlikely past the critical threshold.[Hacker News]