No percolation at criticality on quasi-transitive graphs
Source: github.com/openai/math/tree/main/preprints/No-percolation-a…
We prove that critical Bernoulli bond percolation has no infinite cluster on any infinite connected locally finite quasi-transitive graph with critical probability less than one. This resolves the bond form of the criticality conjecture of Benjamini and Schramm.
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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…