A Count Probability Cookbook: Spurious Effects and the Scaling Model

Abstract

We study the errors brought by finite volume effects and dilution effects on the practical determination of the count probability distribution function P_N(n,L), which is the probability of having N objects in a cell of volume L^3 for a set of average number density n. Dilution effects are particularly relevant to the so-called sparse sampling strategy. This work is mainly done in the framework of the scaling model (Balian \& Schaeffer 1989), which assumes that the Q-body correlation functions obey the scaling relation xi_Q(K r_1,..., K r_Q) = K^{-(Q-1) gamma} xi_N(r_1,..., r_Q). We use three synthetic samples as references to perform our analysis: a fractal generated by a Rayleigh-Lévy random walk with 3.10^4 objects, a sample dominated by a spherical power-law cluster with 3.10^4 objects and a cold dark matter (CDM) universe involving 3.10^5 matter particles.

44 pages, uuencoded compressed postcript file, FERMILAB-Pub-94/229-A, accepted in ApJS

Cited by in corpus (33)

• The density and peculiar velocity fields of nearby galaxies
• Non-Linear Evolution of the Bispectrum of Cosmological Perturbations
• The Bispectrum: From Theory to Observations
• Probability Distribution Function of Cosmological Density Fluctuations from Gaussian Initial Condition: Comparison of One- and Two-point Log-normal Model Predictions with N-body Simulations
• Fisher for complements: Extracting cosmology and neutrino mass from the counts-in-cells PDF
• Statistics of Weak Lensing at Small Angular Scales: Analytical Predictions for Lower Order Moments
• Effects of Sampling on Statistics of Large Scale Structure
• Cosmic Statistics of Statistics
• Quantification of discreteness effects in cosmological N-body simulations: I. Initial Conditions
• Scaling in Gravitational Clustering, 2D and 3D Dynamics
• Experimental Cosmic Statistics II: Distribution
• Experimental Cosmic Statistics I: Variance
• From Snakes to Stars, the Statistics of Collapsed Objects - II. Testing a Generic Scaling Ansatz for Hierarchical Clustering
• How to Optimally Constrain Galaxy Assembly Bias: Supplement Projected Correlation Functions with Count-in-cells Statistics
• Weak lensing shear and aperture-mass from linear to non-linear scales
• Galaxy Clustering and Dark Energy
• Probing The Gravity Induced Bias with Weak Lensing: Test of Analytical results Against Simulations
• How Sensitive Are Weak Lensing Statistics to Dark Energy Content?
• The large-scale correlations of multi-cell densities and profiles, implications for cosmic variance estimates
• Error Estimates for Measurements of Cosmic Shear
• Statistical Tests for CHDM and \LambdaCDM Cosmologies
• The Variance and Covariance of Counts-in-Cells Probabilities
• Cosmic Statistics through Weak Lenses
• The redshift evolution of bias and baryonic matter distribution
• Void Statistics and Hierarchical Scaling in the Halo Model
• Impact of tidal environment on galaxy clustering in GAMA
• Cross-correlating Sunyaev-Zel'dovich and Weak Lensing Maps
• New Statistical Perspective to The Cosmic Void Distribution
• Covariances of density probability distribution functions. Lessons from hierarchical models
• One-point Statistics of the Cosmic Density Field in Real and Redshift Spaces with A Multiresolutional Decomposition
• Ultraviolet background fluctuations with clustered sources
• Effects of Smoothing Functions in Cosmological Counts-in-Cells Analysis
• Void probability function in the Quijote simulations