Universal correlators and distributions as experimental signatures of 2+1 Kardar-Parisi-Zhang growth

We examine height-height correlations in the transient growth regime of the 2+1 Kardar-Parisi-Zhang (KPZ) universality class, with a particular focus on the {\it spatial covariance} of the underlying two-point statistics, higher-dimensional analog of the 1+1 KPZ Class Airy$_1$ process. Making comparison to AFM kinetic roughening data in 2d organic thin films, we use our universal 2+1 KPZ spatial covariance to extract key scaling parameters for this experimental system. Additionally, we explore the i) height, ii) local roughness, and iii) extreme value distributions characteristic of these oligomer films, finding compelling agreement in all instances with our numerical integration of the KPZ equation itself. Finally, investigating nonequilibrium relaxation phenomena exhibited by 2+1 KPZ Class models, we have unearthed a universal KPZ ageing kinetics. In experiments with ample data in the time domain, our 2+1 KPZ Euler {\it temporal covariance} will allow a quick, independent estimate of the central KPZ scaling parameter.