{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"0cae67b4a41a773f871cbe1e2a8f9ef5fa33cd05c41069a55aad0edf36f34a79","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"80fa105755dc8af63bb151fe502386a250dcbb3a0f5ec4edc8852100b9a5ae87","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"stat.extreme-events-predictability.instanton-dominance","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"For very rare large events in noisy or chaotic systems, theory often assumes they occur along one most likely route, called an instanton. Whether and when that holds in high-dimensional systems like turbulence decides whether extremes can be computed rather than waited for.","posed_since":"","precise":"For stochastically forced systems (Burgers, 2D and 3D Navier-Stokes with Gaussian forcing of strength $\\epsilon$) and for deterministic chaotic systems, determine the observables $O$ and thresholds $z$ for which $P(O > z)$ is given asymptotically ($z \\to \\infty \\text{ or } \\epsilon \\to 0$) by a single minimizer of the Freidlin-Wentzell action, including the prefactor, and characterize failures due to fluctuations around the instanton or several competing paths. An answer is a classification with verified prefactors.","problem_ref":null,"references":"","settled_by":"Comparison of instanton predictions, including prefactors, with rare-event sampling of tails over many orders of magnitude for a set of flows and observables.","status_note":"Instanton predictions match velocity-gradient tails in Burgers turbulence and some 2D flows; extremes in 3D Navier-Stokes turbulence are not settled.","title":"When single optimal paths dominate extreme events","topic_ref":"3cc2a242217c0631de30c1e7f17b417925702a48deedb658cb354b09c691f239"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"392d4b01577258ea5facbb8ff873d557924801e8a6c77ec292982944186c1fa7","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"c3d9fc017750f88b33cb51b5750e5bbfeaafa412987f95f1fdeb714d21c9a215","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"MCH5dS93mXX_MxEoqBDte7DGrqNJ_5dGrVIXePTQA92QnVBTW9IFY5gQjbfSmz4M8OlJHW-y_8p1YxcJPGCkCg"},"schema":"pubphys.envelope/1"},"record_hash":"392d4b01577258ea5facbb8ff873d557924801e8a6c77ec292982944186c1fa7","leaf_index":2076}