Statistics of Fourier Modes in Non-Gaussian Fields

Abstract

Fourier methods are fundamental tools to analyze random fields. Statistical structures of homogeneous Gaussian random fields are completely characterized by the power spectrum. In non-Gaussian random fields, polyspectra, higher-order counterparts of the power spectrum, are usually considered to characterize statistical information contained in the fields. However, it is not trivial how the Fourier modes are distributed in general non-Gaussian fields. In this paper, distribution functions of Fourier modes are directly considered and their explicit relations to the polyspectra are given. Under the condition that any of the polyspectra does not diverge, the distribution function is expanded by dimensionless combinations of polyspectra and a total volume in which the Fourier transforms are performed. The expression up to second order is generally given, and higher-order results are also derived in some cases. A concept of N-point distribution function of Fourier modes are introduced and explicitly calculated. Among them, the one-point distribution function is completely given in a closed form up to arbitrary order. As an application, statistics of Fourier phases are explored in detail. A number of aspects regarding statistical properties of phases are found. It is clarified, for the first time, how phase correlations arise in general non-Gaussian fields. Some of our analytic results are tested against numerical realizations of non-Gaussian fields, showing good agreements.

37 pages, 23 figures

References in corpus (8)

• Phase Information and the Evolution of Cosmological Density Perturbations
• Self-Similar Evolution of Gravitational Clustering: N-Body Simulations of the n=-2 Spectrum
• Diagrammatic Methods in Statistics and Biasing in the Large-scale Structure of the Universe
• Statistical Cosmology with Quadratic Density Fields
• Universal Behavior of Phase Correlations in Non-linear Gravitational Clustering
• Phase Correlations in Non-Gaussian Fields
• Fourier Phase Analysis of SDSS Galaxies
• The Distribution Function of the Phase Sum as a Signature of Phase Correlations Induced by Nonlinear Gravitational Clustering

Cited by in corpus (20)

• The Primordial Black Hole Dark Matter - LISA Serendipity
• The power spectrum and bispectrum of SDSS DR11 BOSS galaxies I: bias and gravity
• Testing Primordial Black Holes as Dark Matter through LISA
• Dark matter and halo bispectrum in redshift space: theory and applications
• Simulations of Baryon Acoustic Oscillations I: Growth of Large-Scale Density Fluctuations
• The DESI $N$-body Simulation Project -- II. Suppressing sample variance with fast simulations
• Cosmology with Phase Statistics: Parameter Forecasts and Detectability of BAO
• Statistical connection of peak counts to power spectrum and moments in weak lensing field
• Indra: a Public Computationally Accessible Suite of Cosmological $N$-body Simulations
• Accurate field-level weak lensing inference for precision cosmology
• The cosmic spiderweb: equivalence of cosmic, architectural, and origami tessellations
• Perturbative Gaussianizing transforms for cosmological fields
• Psi-GAN: A power-spectrum-informed generative adversarial network for the emulation of large-scale structure maps across cosmologies and redshifts
• Higher-Order Spectra of Weak Lensing Convergence Maps in Parameterized Theories of Modified Gravity
• Frequency-Domain Distribution of Astrophysical Gravitational-Wave Backgrounds
• Numerical investigation of non-Gaussianities in the phase and modulus of density Fourier modes
• Structure in Galaxy Distribution. III. Fourier Transforming the Universe
• A New Estimator for Phase Statistics
• About One-point Statistics of the Ratio of Two Fourier-transformed Cosmic Fields and an Application
• On Weak Lensing Response Functions