Diagrammatic Methods in Statistics and Biasing in the Large-scale Structure of the Universe

Abstract

We develop technique concerning statistical analyses of the large-scale structure of the universe in the presence of biasing in the structure formation. We formulate the diagrammatic method to calculate the correlation functions of the nonlocally biased field from a generally non-Gaussian density field. Our method is based on generalized Wiener-Hermite expansion of the density field. The present formalism has not only general applicability, but also practical significance, too. To show the effectiveness of this method, we revisit the problems on biasing that have been considered previously, i.e., various approximations for peak statistics and hierarchical structure of correlation functions of locally biased field. Further analyses which have not been possible so far on these problems can be performed by our formalism. The gravitational evolution of primordial fluctuation or other structure-forming processes can be described by nonlocal biasing, so can be treated by our new formalism in principle.

40 pages + 13 figures (uuencoded postscript)

Cited by in corpus (40)

• Large-Scale Galaxy Bias
• Clustering of dark matter tracers: generalizing bias for the coming era of precision LSS
• Gravity and Large-Scale Non-local Bias
• Multi-Point Propagators in Cosmological Gravitational Instability
• Primordial non-Gaussianity: large-scale structure signature in the perturbative bias model
• Physical Bayesian modelling of the non-linear matter distribution: new insights into the Nearby Universe
• Nonlinear Perturbation Theory Integrated with Nonlocal Bias, Redshift-space Distortions, and Primordial Non-Gaussianity
• Primordial Non-Gaussianity and Analytical Formula for Minkowski Functionals of the Cosmic Microwave Background and Large-scale Structure
• Peak-Background Split, Renormalization, and Galaxy Clustering
• Stochasticity of Bias and Nonlocality of Galaxy Formation: Linear Scales
• Bias Loop Corrections to the Galaxy Bispectrum
• A halo bias function measured deeply into voids without stochasticity
• Testing one-loop galaxy bias: joint analysis of power spectrum and bispectrum
• The Monopole Moment of the Three-Point Correlation Function of the 2-degree Field Galaxy Redshift Survey
• Scale Dependence of Halo Bispectrum from Non-Gaussian Initial Conditions in Cosmological N-body Simulations
• Scale dependent halo bias in the excursion set approach
• A General Formulation of the Source Confusion Statistics and Application to Infrared Galaxy Surveys
• Testing one-loop galaxy bias: Power spectrum
• Integrated Perturbation Theory and One-loop Power Spectra of Biased Tracers
• Towards a self-consistent analysis of the anisotropic galaxy two- and three-point correlation functions on large scales: application to mock galaxy catalogues
• Non-Gaussianity in Large Scale Structure and Minkowski Functionals
• A local bias approach to the clustering of discrete density peaks
• On Recovering the Nonlinear Bias Function from Counts in Cells Measurements
• Lagrangian bias of generic large-scale structure tracers
• Phase Correlations in Non-Gaussian Fields
• Halo Sampling, Local Bias and Loop Corrections
• Clustering of primordial black holes formed in a matter-dominated epoch
• Three-point phase correlations: A new measure of non-linear large-scale structure
• Observational Constraints on Higher Order Clustering up to $z\simeq 1
• Statistics of Fourier Modes in Non-Gaussian Fields
• The Distribution Function of the Phase Sum as a Signature of Phase Correlations Induced by Nonlinear Gravitational Clustering
• Non-Gaussian bias: insights from discrete density peaks
• Integrated perturbation theory for cosmological tensor fields. I. Basic formulation
• The statistics of peaks of weakly non-Gaussian random fields: Effects of bispectrum in two- and three-dimensions
• Integrated perturbation theory for cosmological tensor fields. III. Projection effects
• Non-perturbative halo clustering from cosmological density peaks
• The large-separation expansion of peak clustering in Gaussian random fields
• Bye-bye, Local-in-matter-density Bias: The Statistics of the Halo Field Are Poorly Determined by the Local Mass Density
• Gaussian Lagrangian Galaxy Bias
• Clustering of the extreme: A theoretical description of weak lensing critical points power spectra in the mildly nonlinear regime