On Correlated Random Walks and 21-cm Fluctuations During Cosmic Reionization

Abstract

Analytical approaches to galaxy formation and reionization are based on the mathematical problem of random walks with barriers. The statistics of a single random walk can be used to calculate one-point distributions ranging from the mass function of virialized halos to the distribution of ionized bubble sizes during reionization. However, an analytical calculation of two-point correlation functions or of spatially-dependent feedback processes requires the joint statistics of random walks at two different points. An accurate analytical expression for the statistics of two correlated random walks has been previously found only for the case of a constant barrier height. However, calculating bubble sizes or accurate statistics for halo formation involves more general barriers that can often be approximated as linear barriers. We generalize the two-point solution with constant barriers to linear barriers, and apply it as an illustration to calculate the correlation function of cosmological 21-cm fluctuations during reionization.

10 pages, 4 figures, published in MNRAS

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Cited by in corpus (16)

• 21-cm cosmology
• Reionization and Cosmology with 21 cm Fluctuations
• Fast Large Volume Simulations of the 21 cm Signal from the Reionization and pre-Reionization Epochs
• Anomalous diffusion in correlated continuous time random walks
• The Rise of the First Stars: Supersonic Streaming, Radiative Feedback, and 21-cm Cosmology
• Cosmic Reionization and the 21-cm signal: Comparison between an analytical model and a simulation
• Dark matter halo abundances, clustering and assembly histories at high redshift
• The Difference PDF of 21-cm Fluctuations: A Powerful Statistical Tool for Probing Cosmic Reionization
• Studying the Sources of Cosmic Reionization with 21-cm Fluctuations
• Detecting Early Galaxies Through Their 21-cm Signature
• Measuring the History of Cosmic Reionization using the 21-cm PDF from Simulations
• Radiation-induced large-scale structure during the reionization epoch: the autocorrelation function
• Modification of the 21-cm power spectrum by X-rays during the epoch of reionisation
• The Impact of HI in Galaxies on 21-cm Intensity Fluctuations During the Reionisation Epoch
• The Correlation Between Star Formation and 21cm Emission During the Reionization Epoch
• The Infancy of Cosmic Reionization