Galaxy distribution and extreme-value statistics

Antal, Tibor; Labini, Francesco Sylos; Vasilyev, N. L.; Baryshev, Yu. V.

doi:10.1209/0295-5075/88/59001

Cited by 38 publications

(67 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Extreme value theory is used extensively by weather forecasters, seismologists and actuaries, but less so by cosmologists. However, there are some recent examples of applications to features in the cosmic microwave background (Mikelsons, Silk & Zuntz 2009) and the fluctuations in the density around galaxies (Antal et al 2009). The main result of interest for this paper is the probability distribution of extreme events.…”

Section: Methodsmentioning

confidence: 99%

Are the superstructures in the two-degree field galaxy redshift survey a problem for hierarchical models?

Yaryura¹,

Baugh²,

Angulo³

2011

Monthly Notices of the Royal Astronomical Society

View full text Add to dashboard Cite

We introduce an objective method to assess the probability of finding extreme events in the distribution of cold dark matter such as voids, overdensities or very high mass haloes. Our approach uses an ensemble of N‐body simulations of the hierarchical clustering of dark matter to find extreme structures. The frequency of extreme events, in our case the cell or smoothing volume with the highest count of cluster‐mass dark matter haloes, is well described by a Gumbel distribution. This distribution can then be used to forecast the probability of finding even more extreme events, which would otherwise require a much larger ensemble of simulations to quantify. We use our technique to assess the chance of finding concentrations of massive clusters or superclusters, like the two found in the two‐degree field galaxy redshift survey (2dFGRS), using a counts‐in‐cells analysis. The Gumbel distribution gives an excellent description of the distribution of extreme cell counts across two large ensembles of simulations covering different cosmologies, and also when measuring the clustering in both real and redshift space. We find examples of structures like those found in the 2dFGRS in the simulations. The chance of finding such structures in a volume equal to that of the 2dFGRS is around 2 per cent.

show abstract

Section: Methodsmentioning

confidence: 99%

Are the superstructures in the two-degree field galaxy redshift survey a problem for hierarchical models?

Yaryura¹,

Baugh²,

Angulo³

2011

Monthly Notices of the Royal Astronomical Society

View full text Add to dashboard Cite

show abstract

“…When there are long-range correlations of large amplitude the central limit theorem does not hold and fluctuations in global quantities usually have non-Gaussian fluctuations (see Antal et al 2009, for a more detailed discussion).…”

Section: A Brief Summary Of the Statistical Propertiesmentioning

confidence: 99%

Breaking the self-averaging properties of spatial galaxy fluctuations in the Sloan Digital Sky Survey – Data release six

Labini

Vasilyev

Baryshev

2009

A&A

Self Cite

View full text Add to dashboard Cite

Statistical analyses of finite sample distributions usually assume that fluctuations are self-averaging, i.e. statistically similar in different regions of the given sample volume. By using the scale-length method, we test whether this assumption is satisfied in several samples of the Sloan Digital Sky Survey Data Release Six. We find that the probability density function (PDF) of conditional fluctuations, if filtered on large enough spatial scales (i.e., r > 30 Mpc/h), shows relevant systematic variations in different subvolumes of the survey. Instead for scales of r < 30 Mpc/h, the PDF is statistically stable, and its first moment presents scaling behavior with a negative exponent around one. Thus while up to 30 Mpc/h galaxy structures have well-defined power-law correlations, on larger scales it is not possible to consider whole sample average quantities as meaningful and useful statistical descriptors. This situation stems from galaxy structures corresponding to density fluctuations that are too large in amplitude and too extended in space to be self-averaging on such large scales inside the sample volumes: galaxy distribution is inhomogeneous up to the largest scales, i.e. r ≈ 100 Mpc/h probed by the SDSS samples. We show that cosmological corrections, such as K-corrections and standard evolutionary corrections, do not qualitatively change the relevant behaviors. We consider in detail the relation between several statistical measurements generally used to quantify galaxy fluctuations and the scale-length analysis by discussing how the breaking of self-averaging properties makes it impossible to have a reliable estimation of average fluctuations amplitude, variance, and correlations for r > 30 Mpc/h. Finally we show that the large-amplitude galaxy fluctuations observed in the SDSS samples are at odds with the predictions of the standard ΛCDM model of structure formation.

show abstract

“…Because of these large fluctuations in the galaxy density field, self-averaging properties are well-defined only in a limited range of scales. Only in that range it will be statistically meaningful to measure whole-sample average quantities [25,26].…”

Section: P(n;r)mentioning

confidence: 99%

Testing the Copernican and Cosmological Principles in the local universe with galaxy surveys

Labini

Baryshev

2010

J. Cosmol. Astropart. Phys.

View full text Add to dashboard Cite

Cosmological density fields are assumed to be translational and rotational invariant, avoiding any special point or direction, thus satisfying the Copernican Principle. A spatially inhomogeneous matter distribution can be compatible with the Copernican Principle but not with the stronger version of it, the Cosmological Principle which requires the additional hypothesis of spatial homogeneity. We establish criteria for testing that a given density field, in a finite sample at low redshifts, is statistically and/or spatially homogeneous. The basic question to be considered is whether a distribution is, at different spatial scales, self-averaging. This can be achieved by studying the probability density function of conditional fluctuations. We find that galaxy structures in the SDSS samples, the largest currently available, are spatially inhomogeneous but statistically homogeneous and isotropic up to ∼ 100 Mpc/h. Evidences for the breaking of self-averaging are found up to the largest scales probed by the SDSS data. The comparison between the results obtained in volumes of different size allows us to unambiguously conclude that the lack of self-averaging is induced by finite-size effects due to long-range correlated fluctuations. We finally discuss the relevance of these results from the point of view of cosmological modeling.

show abstract

Galaxy distribution and extreme-value statistics

Cited by 38 publications

References 31 publications

Are the superstructures in the two-degree field galaxy redshift survey a problem for hierarchical models?

Are the superstructures in the two-degree field galaxy redshift survey a problem for hierarchical models?

Breaking the self-averaging properties of spatial galaxy fluctuations in the Sloan Digital Sky Survey – Data release six

Testing the Copernican and Cosmological Principles in the local universe with galaxy surveys

Contact Info

Product

Resources

About