What's this about?
A new proof in percolation theory resolves a long-standing question about phase transitions.
What is percolation theory?
The mathematics of connectivity under randomness. Take a grid, keep each connection with probability p, and ask whether a path spans the whole thing. Below a critical p there is no spanning path; above it there is, and the change is abrupt rather than gradual — a phase transition, in the same sense as water freezing. It models fluid through porous rock, forest fire spread, epidemics on networks and conductivity in composites, and its central questions have resisted proof for decades despite being easy to state.
Why is it worth noticing?
HN 52 points, 26 comments
- Phase transitions are the mathematical object underneath a lot of talk about capability jumps in models, usually loosely.
- Quanta remains the only outlet reliably making results like this legible.
- Pure mathematics on a heavy news day, included because it will outlast most of the rest of this digest.