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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 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