Constrained correlation functions

Details Constrained correlation functions Constrained correlation functions

2009-05-05

arxiv.org/abs/0905.0577v1

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

18 pages, 9 figures, submitted to A&A

Scientific paper

We show that correlation functions have to satisfy contraint relations, owing to the non-negativity of the power spectrum of the underlying random process. Specifically, for any statistically homogeneous and (for more than one spatial dimension) isotropic random field with correlation function $\xi(x)$, we derive inequalities for the correlation coefficients $r_n\equiv \xi(n x)/\xi(0)$ (for integer $n$) of the form $r_{n{\rm l}}\le r_n\le r_{n{\rm u}}$, where the lower and upper bounds on $r_n$ depend on the $r_j$, with $j

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