Tracking the origin of black holes with the stochastic gravitational
  wave background popcorn signal
  Unresolved sources of gravitational waves (GWs) produced by the merger of a
binary of black holes at cosmological distances combine into a stochastic
background. Such a background is in the continuous or popcorn regime, depending
on whether the GW rate is high enough so that two or more events overlap in the
same frequency band. These two regimes respectively correspond to large and
small values of the so-called {\it duty cycle}. We study the detection regime
of the background in models of Primordial Black Holes (PBHs) and compare it to
the one produced by black holes of stellar origin. Focusing on ground-based
detectors, we show that the duty cycle of the PBH-origin background is larger
than that of astrophysical black holes because of differences in their mass
function and the merger rate. Our study opens up the possibility to learn about
the primordial or astrophysical nature of black hole populations by examining
the statistical properties of the stochastic background.
