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During cosmic reionization, the 21-cm brightness fluctuations were highlynon-Gaussian, and complementary statistics can be extracted from thedistribution of pixel brightness temperatures that are not derivable from the21-cm power spectrum. One such statistic is the 21-cm difference PDF, theprobability distribution function of the difference in the 21-cm brightnesstemperatures between two points, as a function of the distance between thepoints. Guided by 21-cm difference PDFs extracted from simulations, we performa maximum likelihood analysis on mock observational data, and analyze theability of present and future low-frequency radio array experiments to estimatethe shape of the 21-cm difference PDF, and measure the history of cosmicreionization. We find that one-year data with an experiment such as theMurchison Wide-field Array should suffice for probing large scales during themid-to-late stages of reionization, while a second-generation experiment shouldyield detailed measurements over a wide range of scales during most of thereionization era.

Measuring the History of Cosmic Reionization using the 21-cm Difference PDF