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Lyman-alpha forest lines in QSO spectra have typical widths of 20-50 km/s. Low column density absorbers in cosmological simulations are large, diffuse structures, and the Hubble flow across the spatially extended absorber is usually the dominant contribution to the width of its associated absorption line. Thermal broadening is unimportant over most of the spectrum, and peculiar velocities tend to make absorption features narrower rather than broader. As a consequence of Hubble flow broadening, there is a close relation between local Lyman-alpha optical depth and local neutral hydrogen density, which is well approximated by the Gunn-Peterson formula. The physics that governs the unshocked intergalactic medium leads to a tight correlation between the neutral hydrogen density and the underlying gas and dark matter overdensity. For many purposes, it is simpler to regard a Lyman-alpha forest spectrum as a continuous, non-linear map of the density field rather than a collection of discrete lines. This continuous field view of the Lyman-alpha forest can be applied to measurement of the baryon density parameter, testing of cosmological models, and robust determination of the shape and amplitude of the primordial mass power spectrum.


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