Peak exclusion, stochasticity and convergence of perturbative bias
  expansions in 1+1 gravity
  The Lagrangian peaks of a 1D cosmological random field representing dark
matter are used as a proxy for a catalogue of biased tracers in order to
investigate the small-scale exclusion in the two-halo term. The two-point
correlation function of peaks of a given height is numerically estimated and
analytical approximations that are valid inside the exclusion zone are derived.
The resulting power spectrum of these tracers is investigated and shows clear
deviations from Poisson noise at low frequencies. On large scales, the
convergence of a perturbative bias expansion is discussed. Finally, we go
beyond Gaussian statistics for the initial conditions and investigate the
subsequent evolution of the two-point clustering of peaks through their
Zel'dovich ballistic displacement, to clarify how exclusion effects mix up with
scale-dependencies induced by nonlinear gravitational evolution. While the
expected large-scale separation limit is recovered, significant deviations are
found in the exclusion zone that tends in particular to be reduced at later
times. Even though these findings apply to the clustering of one-dimensional
tracers, they provide useful insights into halo exclusion and its impact on the
two-halo term.
