  We apply the microscopic Bogoliubov theory of dilute Bose-Einstein
condensates to analyze quantum and thermal fluctuations in a flowing atomic
condensate in the presence of a sonic horizon. For the simplest case of a
step-like horizon, closed-form analytical expressions are found for the
spectral distribution of the analog Hawking radiation and for the density
correlation function. The peculiar long-distance density correlations that
appear as a consequence of the Hawking emission features turns out to be
reinforced by a finite initial temperature of the condensate. The analytical
results are in good quantitative agreement with first principle numerical
calculations.
