{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"762954b58a661009a57a2781501fd3953d7ee60dd9aed5c0fcd8c3534bc9077a","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["3ced313b4e02252ba3ae60c140a434adcbe52073d81dfc87f4fdd857b4cfd39f","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"0b66ef7fb21e5c823215deb3c87fcec47b6fb56f98e169af27bf507606ea771a","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":["ai:gpt-5.5"],"external_id":"mathph.quantum-chaos.random-wave-model","kind":"well-posed","literature_status":"open","n":"2","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":"3ced313b4e02252ba3ae60c140a434adcbe52073d81dfc87f4fdd857b4cfd39f","references":"","settled_by":"A proof of Gaussian moments (e.g. $||\\phi_j||_4^4 \\to 3/\\mathrm{vol}(M)$) 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":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"ac3e59277e1911de5d85ce150525628bf7fefe24162c9917e4d1314fad9bd8c8","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"c7d9175666f86c980c6845ca02f2cb7b7383e76f7a5c069e7fcdfc706780bbf2","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"EaUqDMZLhOZKQ63C3WqEPAg6w37YSANzeTk1XOgxddeti6vhWy-Kdfj9bBpsRdzcf71Oh3ZL6gx2z-X9mupUDA"},"schema":"pubphys.envelope/1"},"record_hash":"ac3e59277e1911de5d85ce150525628bf7fefe24162c9917e4d1314fad9bd8c8","leaf_index":3448}