Excursion set approach to the clustering of dark matter haloes in Lagrangian space

We present a stochastic approach to the spatial clustering of dark matter haloes in Lagrangian space. Our formalism is based on a local formulation of the `excursion set' approach by Bond et al., which automatically accounts for the `cloud-in-cloud' problem in the identification of bound systems. Our method allows to calculate correlation functions of haloes in Lagrangian space using either a multi-dimensional Fokker-Planck equation with suitable boundary conditions or an array of Langevin equations with spatially correlated random forces. We compare the results of our method with theoretical predictions for the halo auto-correlation function considered in the literature and find good agreement with the results recently obtained within a treatment of halo clustering in terms of `counting fields' by Catelan et al.. The possible effect of spatial correlations on numerical simulations of halo merger trees is finally discussed.