On the Large-Scale Structure of the Universe as given by the Voronoi Diagrams

Zaninetti, L.

doi:10.1088/1009-9271/6/4/01

Cited by 17 publications

(22 citation statements)

References 23 publications

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“…the least action approach, or Voronoi tessellation techniques [e.g. 132,133,134,135,136,137,138]. A discussion and classification of the various methods can be found in [38].…”

Section: Cosmological Large-scale Structurementioning

confidence: 99%

Information field theory for cosmological perturbation reconstruction and nonlinear signal analysis

2009

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We develop information field theory (IFT) as a means of Bayesian inference on spatially distributed signals, the information fields. A didactical approach is attempted. Starting from general considerations on the nature of measurements, signals, noise, and their relation to a physical reality, we derive the information Hamiltonian, the source field, propagator, and interaction terms. Free IFT reproduces the well known Wiener-filter theory. Interacting IFT can be diagrammatically expanded, for which we provide the Feynman rules in position-, Fourier-, and spherical harmonics space, and the Boltzmann-Shannon information measure. The theory should be applicable in many fields. However, here, two cosmological signal recovery problems are discussed in their IFTformulation. 1) Reconstruction of the cosmic large-scale structure matter distribution from discrete galaxy counts in incomplete galaxy surveys within a simple model of galaxy formation. We show that a Gaussian signal, which should resemble the initial density perturbations of the Universe, observed with a strongly non-linear, incomplete and Poissonian-noise affected response, as the processes of structure and galaxy formation and observations provide, can be reconstructed thanks to the virtue of a response-renormalization flow equation. 2) We design a filter to detect local non-linearities in the cosmic microwave background, which are predicted from some Early-Universe inflationary scenarios, and expected due to measurement imperfections. This filter is the optimal Bayes' estimator up to linear order in the non-linearity parameter and can be used even to construct sky maps of non-linearities in the data.

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“…the least action approach, or Voronoi tessellation techniques [e.g. 132,133,134,135,136,137,138]. A discussion and classification of the various methods can be found in [38].…”

Section: Cosmological Large-scale Structurementioning

confidence: 99%

Information field theory for cosmological perturbation reconstruction and nonlinear signal analysis

2009

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“…N F = 16, see Okabe et al (1992) and Zaninetti (2006). The averaged side of a face of an irregular polyhedron, L V , is…”

Section: The Voronoi Diagramsmentioning

confidence: 99%

“…A great number of natural phenomena are described by Poisson Voronoi diagrams; for example: lattices in quantum field theory, see Drouffe & Itzykson (1984); conductivity and percolation in granular composites, see Jerauld et al (1984aJerauld et al ( , 1984b; modeling growth of metal clusters on amorphous substrates, see Dicenzo & Wertheim (1989); the statistical mechanics of simple glassforming systems in 2D, see Hentschel et al (2007); modeling of material interface evolution in grain growth of polycrystalline materials, see Lee & Chen (2006). A review of Voronoi diagrams applied to the spatial distribution of the galaxies can be found in Zaninetti (2006). Here we are interested in the fragmentation of a 2D layer of thickness negligible with respect to the main dimension.…”

Section: The Voronoi Diagramsmentioning

confidence: 99%

“…Due to the fact that the sum of n independent gamma variates with shape parameter c i is a gamma variate with a shape parameter c = n i c i , the area and the volumes are supposed to follow a gamma variate of argument 4 and 6. This hypothesis was later named "Kiang's conjecture," and Equation (A5) used as a fitting function; see Kumar et al (1992) and Zaninetti (2006), or as a hypothesis to accept or reject using the standard procedures of the data analysis, see Tanemura (1988Tanemura ( , 2003. A new way to parametrize the 1D, 2D, and 3D cells on the base of the considered dimensionality has been introduced; see Formula (12) in Ferenc & Néda (2007).…”

Section: Appendix a The Kiang Functionmentioning

confidence: 99%

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A New Luminosity Function for Galaxies as Given by the Mass-Luminosity Relationship

Zaninetti¹

2008

The Astronomical Journal

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The search for a luminosity function for galaxies both alternative or companion to a Schechter function is a key problem in the reduction of data from catalogs of galaxies. Two luminosity functions for galaxies can be built starting from two distributions of mass as given by the fragmentation. A first overall distribution function is the Kiang function, which represents a useful description of the area and volume distribution of the Poisson Voronoi diagrams. The second distribution, which covers the case of low-mass galaxies, is the truncated Pareto distribution: in this model we have a natural bound due to the minimum mass/luminosity observed and an upper bound (function of the considered environment) represented by the boundary with the observed mass/luminosity overall behavior. The mass distribution is then converted into a luminosity distribution through a standard mass-luminosity relationship. The mathematical rules to convert the probability density function are used and the two new functions are normalized to the total number of galaxies per unit volume. The test of the two new luminosity functions for galaxies that cover different ranges in magnitude was made on the Sloan Digital Sky Survey (SDSS) in five different bands; the results are comparable to those of the Schechter function. A new parameter, which indicates the stellar content, is derived. The joint distribution in redshift and flux, the mean redshift and the number density connected with the first luminosity function for galaxies are obtained by analogy with the Schechter function. A new formula, which allows us to express the mass as a function of the absolute magnitude, is derived.

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“…Polar plot of real galaxies (green points) belonging to the second CFA2 redshift catalog and the simulated galaxies in the PVT framework (red points). More details can be found in Zaninetti (2006). We now test formula (14) in a discrete environment rather than in the continuous case.…”

Section: The Voronoi Simulationmentioning

confidence: 99%

The intergalactic Newtonian gravitational field and the shell theorem

Zaninetti¹

2012

SERBIAN ASTRON J

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The release of the 2MASS Redshift Survey (2MRS) with its 44599 galaxies allows the deduction of their masses in nearly complete sample. A cubic box with side of 37 Mpc containing 2429 galaxies is extracted and the Newtonian gravitational field is evaluated both at the center of the box as well as in 101 x 101 x 101 grid points of the box. The obtained results are then discussed in the light of the shell theorem which states that inside of a sphere the gravitational field is zero

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On the Large-Scale Structure of the Universe as given by the Voronoi Diagrams

Cited by 17 publications

References 23 publications

Information field theory for cosmological perturbation reconstruction and nonlinear signal analysis

Information field theory for cosmological perturbation reconstruction and nonlinear signal analysis

A New Luminosity Function for Galaxies as Given by the Mass-Luminosity Relationship

The intergalactic Newtonian gravitational field and the shell theorem

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