Scale-dependent bias from an inflationary bispectrum: the effect of a
  stochastic moving barrier
  With the advent of large scale galaxy surveys, constraints on primordial
non-Gaussianity (PNG) are expected to reach ${\cal O}(f_\text{NL}) \sim 1$. In
order to fully exploit the potential of these future surveys, a deep
theoretical understanding of the signatures imprinted by PNG on the large scale
structure of the Universe is necessary. In this paper, we explore the effect of
a stochastic moving barrier on the amplitude of the non-Gaussian bias induced
by local quadratic PNG. We show that, in the peak approach to halo clustering,
the amplitude of the non-Gaussian bias will generally differ from the
peak-background split prediction unless the barrier is flat and deterministic.
For excursion set peaks with a square-root barrier, which reproduce reasonably
well the linear bias $b_1$ and mass function $\bar{n}_\text{h}$ of SO haloes,
the non-Gaussian bias amplitude is $\sim 40$% larger than the peak-background
split expectation $d\ln\bar{n}_\text{h}/d\ln\sigma_8$ for haloes of mass $\sim
10^{13} {\it h}^{-1}M_\odot$ at $z=0$. Furthermore, we argue that the effect of
PNG on squeezed configurations of the halo bispectrum differs significantly
from that predicted by standard local bias approaches. Our predictions can be
easily confirmed, or invalidated, with N-body simulations.
