{"id":"openai-math/No-bigeodesics-in-planar-first-passage-percolation","pdf":"https://github.com/openai/math/blob/main/preprints/No-bigeodesics-in-planar-first-passage-percolation-September-24-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/No-bigeodesics-in-planar-first-passage-percolation-September-24-2026","tags":["probability","first-passage-percolation","geodesics"],"score":0,"title":"No bigeodesics in planar first-passage percolation","domain":"Probability and statistical mechanics","family":"212","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We prove that planar first-passage percolation with independent identically distributed nonnegative nonatomic edge weights has almost surely no doubly infinite geodesic, provided the minimum of four independent weights has finite second moment. This resolves the planar no-bigeodesics conjecture under that moment assumption. The conclusion rules out all bigeodesics simultaneously, without any regularity assumption on the limit shape.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-24","reactions":{},"discussion":[{"url":"https://gilkalai.wordpress.com/2026/10/07/updates-sharing-ai-progress-on-mathematics-amazing-and-my-lecture-plans/#:~:text=absence%20of%20doubly%20infinite%20geodesics%20in%20the%20planar%20model","date":"2026-10-07","kind":"web","site":"Combinatorics and more","text":"absence of doubly infinite geodesics in the planar model for i.i.d. nonnegative nonatomic weights whose minimum over four independent samples has finite second moment, and strict convexity and a continuously differentiable limit-shape boundary for exponential weights. Stochastic games and the…","added":"2026-10-24","title":"Updates: Sharing AI progress on mathematics (amazing!); and my lecture plans"}],"formalized":false,"family_title":"Planar first-passage geometry and the absence of bigeodesics"}