The Probability Distribution of Astrophysical Gravitational-Wave
  Background Fluctuations
  The coalescence of compact binary stars is expected to produce a stochastic
background of gravitational waves (GW) observable with future GW detectors.
Such backgrounds are usually characterized by their power spectrum as a
function of frequency. Here, we present a method to calculate the full 1-point
distribution of strain fluctuations. We focus on time series data, but our
approach generalizes to the frequency domain. We illustrate how this
probability distribution can be evaluated numerically. In addition, we derive
accurate analytical asymptotic expressions for the large strain tail, which
demonstrate that it is dominated by the nearest source. As an application, we
calculate the distribution of strain fluctuations for the astrophysical GW
background produced by binary mergers of compact stars in the Universe, and the
distribution of the observed confusion background obtained upon subtracting
bright, resolved sources from the signal. We quantify the extent to which they
deviate from a Gaussian distribution. Our approach could be useful for the
spectral shape reconstruction of stochastic GW backgrounds.
