show that the emission from coexisting individual modes originates from different regions of the same condensate. [@Krizhanovskii.2006; @Baas.2008; @Krizhanovskii.2009] However, other studies on polariton condensates in a disordered environment found that long-range spatial coherence is still present for their energy-averaged emission [@Kasprzak.2006; @Richard.2005] indicating persistent correlations between different, possibly spatially separated condensate states.

For a wide range of excitation powers, condensate emission out of two energy ranges is observed, which are stable and energetically well separated. For a further analysis we select only one of these energy channels, in order to compare with numeric simulations of a single-mode condensate, cf. Sec. \[sec:fit\_of\_exp\_data\]. In Fig. \[fig:Disorder\](b)-(d) we marked the selected energy channel by two white dashed lines. This delimitation is defined by an energy range $\Delta E$ which corresponds to the excitation power dependent full width at half maximum of the condensate emission. Fig. \[fig:Disorder\](e) shows the far field emission profiles $I_P(k)$ for the selected energy channel and increasing excitation power, integrated over $\Delta E$. The $I_P(k)$ profiles show several randomly distributed inhomogeneities and differ strongly from the smooth and ideally radial symmetric distribution expected for a disorder-free sample. [@Wouters.2008] Remarkably, the intensity fluctuations persist even for high excitation power, i.e. 