two-point statistics

I spent the last two days arguing about two-point statistics with Michael Joyce (Paris LPNHE); especially on the remarkable power-law correlation function over five orders of magnitude in separation shown in Masjedi et al, 2006 and our determination of the scale of homogeneity of the Universe (well, of LRGs in the Universe) in Hogg et al, 2005. The integrated "fractal dimension" plot in the latter paper also shows a power-law over a large range of scales, and yet it is a different power than what you would expect naively from the correlation function in the former paper. So there are multiple, unexpected, large-scale power-laws to explain in the clustering in the Universe. In other news, we both lamented the fact that we have no general ways to make (ie, set up in the computer or algorithmically) distributions of points with arbitrary correlation functions.