Measuring 2+1 KPZ statistics beyond flat thin-film growth
In plain words
One-dimensional KPZ laws have been seen in liquid-crystal turbulence and in fluids of light, while two-dimensional tests exist only for flat growing films. A clean experiment in another geometry or system would measure the full statistics of a growing two-dimensional surface or its analog, not only its exponents.
Precise statement
Measure, in a $2+1$ dimensional KPZ system other than flat thin-film deposition (curved or stationary initial geometry, or the phase of a 2D driven-dissipative condensate), the one-point distribution of $\chi$ and the spatial and two-time correlation functions, and compare them with simulated universal functions for that geometry (exponents alpha approximately 0.39, z approximately 1.61).
What would settle it
A measurement whose distribution of $\chi$, including skewness and kurtosis, and whose two-time correlations agree with simulations for the matching geometry within experimental error.
Status in the literature
Unverified note
Height distributions matching 2+1 KPZ simulations were measured in CdTe thin films (Almeida, Ferreira, Oliveira, Aarao Reis, Phys. Rev. B 89, 045309, 2014); a 2025 exciton-polariton experiment reported 2D KPZ scaling of phase correlations (arXiv:2506.15521); curved and stationary geometries and two-time statistics remain untested.