Non-Gaussian bias: insights from discrete density peaks
  Corrections induced by primordial non-Gaussianity to the linear halo bias can
be computed from a peak-background split or the widespread local bias model.
However, numerical simulations clearly support the prediction of the former, in
which the non-Gaussian amplitude is proportional to the linear halo bias. To
understand better the reasons behind the failure of standard Lagrangian local
bias, in which the halo overdensity is a function of the local mass overdensity
only, we explore the effect of a primordial bispectrum on the 2-point
correlation of discrete density peaks. We show that the effective local bias
expansion to peak clustering vastly simplifies the calculation. We generalize
this approach to excursion set peaks and demonstrate that the resulting
non-Gaussian amplitude, which is a weighted sum of quadratic bias factors,
precisely agrees with the peak-background split expectation, which is a
logarithmic derivative of the halo mass function with respect to the
normalisation amplitude. We point out that statistics of thresholded regions
can be computed using the same formalism. Our results suggest that halo
clustering statistics can be modelled consistently (in the sense that the
Gaussian and non-Gaussian bias factors agree with peak-background split
expectations) from a Lagrangian bias relation only if the latter is specified
as a set of constraints imposed on the linear density field. This is clearly
not the case of standard Lagrangian local bias. Therefore, one is led to
consider additional variables beyond the local mass overdensity.
