{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"2b83664e7416d28663bd9ce696b1a88646493e187659a4fb43c881d1789b6938","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"41e5c838bc6985917d8fcf12fa030db45197f6bbb7ce202ed496c2b62a0fa383","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"mathph.quantum-chaos.random-wave-model","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Berry proposed that a high-frequency standing wave of a chaotic system looks locally like a random superposition of plane waves, so its values follow a bell curve. Even a much weaker consequence, that no eigenfunction has unusually high peaks, is unproven.","posed_since":"1977","precise":"Compact negatively curved surface $M$ (or an ergodic billiard), $-\\operatorname{Lap} \\phi_{j} = \\lambda_{j} \\phi_{j}$, $||\\phi_{j}||_{2} = 1$. Prove that for a density-one subsequence the distribution of $\\phi_{j}(x)$, $x$ uniform on $M$, converges to the Gaussian of variance $1/\\operatorname{vol}(M)$; a weaker target is the sup-norm bound ||phi_j||_inf <= C_eps lambda_j^eps. Answer: a proof.","problem_ref":null,"references":"","settled_by":"A proof of Gaussian moments (e.g. ||phi_j||_4^4 -> 3/vol(M)) for a density-one subsequence on one negatively curved surface.","status_note":"The general sup-norm bound is $\\lambda^{1/4}$ up to logarithmic improvement; on arithmetic surfaces Iwaniec and Sarnak (1995) proved $\\lambda^{5/24+\\varepsilon}$.","title":"Gaussian value distribution of chaotic eigenfunctions","topic_ref":"ea13ab5f74a1c82c80da965948277a56b113b5df57a11f41c996b317accddd90"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"3ced313b4e02252ba3ae60c140a434adcbe52073d81dfc87f4fdd857b4cfd39f","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"0a33ef5622f0f79072dc0c270207e9a890cdd6788cd292f14a1e4c3d348190a7","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"5IdRwm1hDaCkLmRArgit8EYls1R1VbfR6w1oOcwj9LsQKk53LfCy1Ox581G2oxsgPsGDPlh3-cGVQZ_4A1jsDw"},"schema":"pubphys.envelope/1"},"record_hash":"3ced313b4e02252ba3ae60c140a434adcbe52073d81dfc87f4fdd857b4cfd39f","leaf_index":1651}