In arXiv:0904.3098 Lin, Ostriker & Miller use a cluster catalog, assemblked from SDSS DR5 to examine the question whether or not BCGs are just the statistical extremes from the luminosity distributions of cluster galaxies, or whether they are really distinct objects. They do a very simple test: they throw together all cluster galaxies, and randomly sample luminosities from this distribution, adding up to the total luminosities of clusters. They then compare the statistic d in this plot. d is the difference in log between the mean luminosity of observed(blue)/sampled(red) BCGs and of 200 MC realizationsof this process. The red line therefore should be centered on zero, and it is. The offset of the blue histogram is significant in the total sample (494 clusters) and in the sample of bright clusters (124 clusters). FOr the total sample they calculate a probablity of less than 0.8% that the distributions come from the same parent distribution, for the bright subsample it is 0.03%. For low luminosity clusters there is no significant deviation between the two (P = 54.5%). They therefore claim that (at least for the bright ones) BCGs must evolve distinct from the rest of the galaxy population, making them brighter than their non-BCG cluster companions.
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