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We measure the Voronoi density probability distribution function (PDF) forboth dark matter and halos in N-body simulations. For the dark matter, Voronoidensities represent the matter density field smoothed on a uniform mass scale,which approximates the Lagrangian density field. For halos, the Voronoidensities contain information about the local environment of each halo. Wemeasure the halo virial masses, the total amount of dark matter within eachhalo Voronoi cell, and the halo Voronoi cell volumes, and we show how haloabundances depend on these three quantities. We then study theposition-dependent Voronoi density PDF, measured within finite subregions ofthe Universe, using separate universe simulations. We demonstrate that thespatial variation of the position-dependent PDF is due to large-scale densityfluctuations, indicating that the position-dependent PDF is a biased tracer oflarge-scale structure. We measure this bias for the dark matter, and interpretit as the bias of regions of the Lagrangian density field that are selectedbased on density. For the halos, this bias can be interpreted as a form ofassembly bias. We present the mapping from late-time to early-time Voronoidensity for each simulation dark matter particle, which is highly stochastic.We compare the median of this stochastic map with spherical collapsecalculations and discuss challenges involved in modeling the evolution of thedensity field on these scales.

Position-dependent Voronoi probability distribution functions for matter and halos