One- and Two-point Source Statistics from the LOFAR Two-metre Sky Survey
  First Data Release
  The LOFAR Two-metre Sky Survey (LoTSS) will map the complete Northern sky and
provide an excellent opportunity to study the distribution and evolution of the
large-scale structure of the Universe. We study the completeness of the LoTSS
first data release (DR1) and find a point-source completeness of 99 % above
flux densities of 0.8 mJy and define a suite of quality cuts. We determine the
count-in-cell statistics and differential source counts statistic and measure
the angular two-point correlation function of the LoTSS radio sources. The
counts-in-cell statistic reveals that the distribution of radio sources cannot
be described by a spatial Poisson process. Instead, a good fit is provided by a
compound Poisson distribution. The differential source counts are in good
agreement with previous findings in deep fields at low radio frequencies and
with simulated catalogues from the SKA design study sky and the Tiered Radio
Extragalactic Continuum Simulation. The angular two-point correlation is
$<10^{-2}$ at angular scales $> 1$ deg. Restricting the value added source
catalogue to low-noise regions and a flux density threshold of 2 mJy provides
our most reliable estimate of the angular two-point correlation. For smaller
flux density thresholds systematic issues are identified, most likely related
to the flux density calibration of the individual pointings. Based on the
distribution of photometric redshifts of LoTSS sources and the Planck 2018
best-fit cosmological model, the theoretically predicted angular two-point
correlation between 0.1 deg and 6 deg agrees with the measured clustering for a
subsample of radio sources with redshift information. We find agreement with
the expectation of large-scale statistical isotropy of the radio sky at the per
cent level. The angular two-point correlation agrees well with the expectation
of the cosmological standard model. (abbreviated)
