  False vacuum decay in quantum mechanical first order phase transitions is a
phenomenon with wide implications in cosmology, and presents interesting
theoretical challenges. In the standard approach, it is assumed that false
vacuum decay proceeds through the formation of bubbles that nucleate at random
positions in spacetime and subsequently expand. In this paper we investigate
the presence of correlations between bubble nucleation sites using a recently
proposed semi-classical stochastic description of vacuum decay. This procedure
samples vacuum fluctuations, which are then evolved using classical lattice
simulations. We compute the two-point function for bubble nucleation sites from
an ensemble of simulations, demonstrating that nucleation sites cluster in a
way that is qualitatively similar to peaks in random Gaussian fields. We
qualitatively assess the phenomenological implications of bubble clustering in
early Universe phase transitions, which include features in the power spectrum
of stochastic gravitational waves and an enhancement or suppression of the
probability of observing bubble collisions in the eternal inflation scenario.
