Position-dependent Voronoi probability distribution functions for matter and halos

We measure the Voronoi density probability distribution function (PDF) for both dark matter and halos in N-body simulations. For matter, densities represent field smoothed on a uniform mass scale, which approximates Lagrangian field. halos, contain information about local environment of each halo. halo virial masses, total amount within cell, cell volumes, we show how abundances depend these three quantities. then study position-dependent PDF, measured finite subregions Universe, using separate universe demonstrate that spatial variation PDF is due to large-scale fluctuations, indicating biased tracer structure. this bias interpret it as regions are selected based density. can be interpreted form assembly bias. present mapping from late-time early-time simulation particle, highly stochastic. compare median stochastic map with spherical collapse calculations discuss challenges involved modeling evolution scales.