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Statistical analyses of finite sample distributions usually assume thatfluctuations are self-averaging, i.e. that they are statistically similar indifferent regions of the given sample volume. By using the scale-length method,we test whether this assumption is satisfied in several samples of the SloanDigital Sky Survey Data Release Six. We find that the probability densityfunction (PDF) of conditional fluctuations, filtered on large enough spatialscales (i.e., r>30 Mpc/h), shows relevant systematic variations in differentsub-volumes of the survey. Instead for scales r<30 Mpc/h the PDF isstatistically stable, and its first moment presents scaling behavior with anegative exponent around one. Thus while up to 30 Mpc/h galaxy structures havewell-defined power-law correlations, on larger scales it is not possible toconsider whole sample average quantities as meaningful and useful statisticaldescriptors. This situation is due to the fact that galaxy structurescorrespond to density fluctuations which are too large in amplitude and tooextended in space to be self-averaging on such large scales inside the samplevolumes: galaxy distribution is inhomogeneous up to the largest scales, i.e. r~ 100 Mpc/h, probed by the SDSS samples. We show that cosmological corrections,as K-corrections and standard evolutionary corrections, do not qualitativelychange the relevant behaviors. Finally we show that the large amplitude galaxyfluctuations observed in the SDSS samples are at odds with the predictions ofthe standard LCDM model of structure formation.(Abridged version).

Breaking the self-averaging properties of spatial galaxy fluctuations in the Sloan Digital Sky Survey - Data Release Six