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Most massive haloes with Gumbel statistics




We present an analytical calculation of the extreme value statistics for dark matter haloes – i.e., the probability distribution of the most massive halo within some region of the universe of specified shape and size. Our calculation makes use of the counts-in-cells formalism for the correlation functions, and the halo bias derived from the Sheth–Tormen mass function.

We demonstrate the power of the method on spherical regions, comparing the results to measurements in a large cosmological dark matter simulation and achieving good agreement. Particularly good fits are obtained for the most likely value of the maximum mass and for the high-mass tail of the distribution, relevant in constraining cosmologies by observations of most massive clusters.