The joint gluing inequality in the language of Green's functions
The joint gluing inequality is the step that my animated tour of the θ(p_c) = 0 proof calls the hard part. I wrote a short note that retells OpenAI’s proof of it in the language of Markov-chain potential theory: Green functions, killed chains, excessive functions and the Poisson equation. Probabilists who work with random walks already speak this language. The note is an exposition. The estimates and key identities are OpenAI’s, and it claims no new theorem. It adds only a change of language and a few elementary rearrangements, which it flags as such. Read the note (7 pages): Zenodo, doi:10.5281/zenodo.24062184 · PDF ...