Astronomy and Astrophysics – Astrophysics
Scientific paper
2002-10-31
Astronomy and Astrophysics
Astrophysics
7 pages, 1 figure, proceedings of the 7th Granada Seminar of Computational and Statistical Physics (2002, Spain)
Scientific paper
10.1063/1.1571311
After reviewing some basic relevant properties of stationary stochastic processes (SSP), we discuss the properties of the so-called Harrison-Zeldovich like spectra of mass density perturbations. These correlations are a fundamental feature of all current standard cosmological models. Examining them in real space we note they imply a "sub-poissonian" normalised variance in spheres $\sigma_M^2(R) \sim R^{-4} \ln R$. In particular this latter behaviour is at the limit of the most rapid decay ($\sim R^{-4}$) of this quantity possible for any stochastic distribution (continuous or discrete). In a simple classification of all SSP into three categories, we highlight with the name ``super-homogeneous'' the properties of the class to which models like this, with $P(0)=0$, belong. In statistical physics language they are well described as lattice or glass-like. We illustrate their properties through two simple examples: (i) the ``shuffled'' lattice and the One Component Plasma at thermal equilibrium.
Gabrielli Andrea
Joyce Michael
Sylos Labini Francesco
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