Measuring nonlocal Lagrangian peak bias factors

In the Lagrangian approach to halo clustering, nonlocal bias can be generated either
in the initial conditions or by the subsequent gravitational motions. Here, we investi-
gate nonlocal Lagrangian bias contributions involving gradients of the linear density
eld, for which we have predictions from the excursion set peak formalism. We refor-
mulate this approach in order to explicitly take into account the variable describing
the crossing of the collapse barrier. This enables us to write down a bias expansion
which includes all the bias terms, including the nonlocal ones. Having checked that
the model furnishes a reasonable t to the halo mass function, we extend the 1-point
cross-correlation technique of Musso, Paranjape & Sheth (2012) to bias contributions
that are chi-squared distributed. We validate the method with numerical realizations
of peaks of Gaussian random elds before applying it to N-body simulations. We focus
on the lowest (quadratic) order nonlocal bias factors predicted by the excursion set
peaks approach. While the measurements are qualitatively consistent with the theo-
retical predictions, they point to the need for a rened description of the Lagrangian
patches that collapse into haloes.