Progress report: probabilistic and statistical bases of surface brightness fluctuations

The surface brightness fluctuations (SBF) method is a statistical method applied on image pixels in different bands. This contribution aims to distinguish between the observational (statistical) method and the theoretical (probabilistic) method based on stellar population synthesis and needed for the calibration of observational SBF. We find that the commonly used SBF theoretical definition as the "mean luminosity-weighted luminosity of the stellar population" is only compatible with the observational method under quite strong hypotheses, and that it is not compatible with stellar population theory results.