{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"9993a2d8b22c77f2dc16af883b9cd69895d0110ed0f36b1ab9544ca2678fafda","created":"2026-10-03T07:18:11Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"61ee239116a9d574fa7c612f21b84842cc0d6cecdf74881155dfc7ca4178e8f4","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"identification","assisted_by":[],"external_id":"stat.kpz-higher-d.height-distribution-2plus1","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"In one dimension the rescaled height of a KPZ surface follows the Tracy-Widom distributions of random matrix theory (the statistics of the largest eigenvalue of a large random matrix). In two dimensions the corresponding universal distributions are measured numerically but have no known formula.","posed_since":"","precise":"For KPZ growth in $d = 2$ with flat, curved (radial) and stationary initial conditions, write $h(x,t)=v t+(\\Gamma t)^{\\beta}\\chi$ and identify the limiting distribution of $\\chi$ in each geometry, together with its spatial and temporal correlation functions, and determine whether it has a solvable structure such as a Fredholm determinant or determinantal point process. An answer is an explicit distribution matching simulations.","problem_ref":null,"references":"","settled_by":"An exact derivation of the distribution for one solvable 2+1 model, or a closed form that matches high-precision simulations in all moments.","status_note":"","title":"Universal height distributions of KPZ surfaces in 2+1 dimensions","topic_ref":"26996c76133d5f7829488e993c1a11588f8ba15e793c45cb8f57b08744ba791a"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"d6a2e81028c511572d61756b3d676b513ac5a58da8e7776d40d82896aec7f4e1","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"577a611a1fb972e00ec2b71b45a744fd63c8557a68495345d366a675dd7428d9","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"Fzw-nJwRULKgIBvCOf_gKVYXd_jxP119WBccpD6KpHuWuvEamLaanAK6Rbodz7jWdgcVWcXq5f7lcCi-iRTDBg"},"schema":"pubphys.envelope/1"},"record_hash":"d6a2e81028c511572d61756b3d676b513ac5a58da8e7776d40d82896aec7f4e1","leaf_index":2087}