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## Homogeneity, features

Yesterday I read a few of the recent papers of Francesco Sylos Labini, who has pursued a distinction between the common or garden type statistical homogeneity in the Universe that one reads about in textbooks, and a stronger form (‘super-homogeneity’) in which the mass fluctuations follow a behaviour that is sub-Poisson as a function of scale. This implies a sort of anti-correlation—a lattice of points is, for instance, sub-Poisson, as the points are deliberately avoiding one another—and has consequences for the form of the two-point correlation function:

$\int \xi(r) d^3 r = 0$

that look remarkably similar to those imposed by the integral constraint, but which are, in fact, quite different—the super-homogeneity condition affects the actual correlation function, while the correction usually referred to as the integral constraint affects estimators of the correlation function. I started writing a summary document on this topic for the reference of myself and others.

After DARK’s infamous $\gamma\Lambda$ session, I hit a sweet spot in coding productivity and wrote a bunch of scripts to extract spatial features from galaxy images, along lines suggested to me a week or so ago by Andrew Zirm. These features are extracted from a matrix that encodes the frequency of adjacency between threshold intensity levels in the image. It’s the sort of thing best shown with pictures, which perhaps I can post once Andrew has decided which direction to pursue next.