Double Distribution of Dark Matter Halos with respect to Mass and Local   Overdensity
  We present a double distribution function of dark matter halos, with respect to both object mass and local over- (or under-) density. This analytical tool provides a statistical treatment of the properties of matter surrounding collapsed objects, and can be used to study environmental effects on hierarchical structure formation. The size of the "local environment" of a collapsed object is defined to depend on the mass of the object. The Press-Schechter mass function is recovered by integration of our double distribution over the density contrast. We also present a detailed treatment of the evolution of overdensities and underdensities in Einstein-deSitter and flat LCDM universes, according to the spherical evolution model. We explicitly distinguish between true and linearly extrapolated overdensities and provide conversion relations between the two quantities. 
Vasiliki Pavlidou and Brian D. Fields (University of Illinois at   Urbana-Champaign)