However, recent theoretical studies have revealed exciting differences between equilibrium and non-equilibrium condensates [@Sieberer.2013; @Sieberer.2014; @Tauber.2014; @Altman.2013; @Janot.2013]. For example, it is predicted that correlation functions for the condensate wave function decay exponentially [@Altman.2013] and that superfluidity vanishes in the presence of disorder. [@Janot.2013]

A polariton BEC is a steady state out of equilibrium where losses are compensated by external excitation. In the presence of disorder, spatial inhomogeneities of the condensate phase are induced. [@Janot.2013] If the phase fluctuates on length scales comparable to the condensate size, spatial correlations and phase rigidity are strongly reduced. In our work we will show that this leads to significant traces of disorder in the experimentally observed $k$-space intensity distribution, and theoretically demonstrate that the ratio of the condensate correlation length to the condensate size is independent of the condensate density. Consequently, in polariton condensates the stabilization against disorder fluctuations with increasing condensate density is strongly suppressed as compared to condensates in equilibrium. This prediction is supported by experimental investigations of the impact of disorder on a two-dimensional polariton BEC in a ZnO based MC. We measure the $k$-space intensity distribution as a function of excitation power, or rather condensate density, and observe significant 