Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Environmental dependence in the ellipsoidal collapse model   N-body simulations have demonstrated a correlation between the properties of
haloes and their environment. In this paper, we assess whether the ellipsoidal
collapse model can produce a similar dependence. First, we explore the
statistical correlation that originates from Gaussian initial conditions. We
derive analytic expressions for a number of joint statistics of the shear
tensor and estimate the sensitivity of the local characteristics of the shear
to the global geometry of the large scale environment. Next, we concentrate on
the dynamical aspect of the environmental dependence using a simplified model
that takes into account the interaction between a collapsing halo and its
environment. We find that the tidal force exerted by the surrounding mass
distribution causes haloes embedded in overdense regions to virialize earlier.
An effective density threshold whose shape depends on the large scale density
provides a good description of this environmental effect. We show that, using
this approach, a correlation between formation redshift, large scale bias and
environment density naturally arises. The strength of the effect is comparable,
albeit smaller, to that seen in simulations. It is largest for low mass haloes
and decreases as one goes to higher mass objects. Furthermore, haloes that
formed early are substantially more clustered than those that assembled
recently. On the other hand, our analytic model predicts a decrease in median
formation redshift with increasing environment density, in disagreement with
the trend detected in overdense regions. However, our results appear consistent
with the behaviour inferred in relatively underdense regions. We argue that the
ellipsoidal collapse model may apply in low density environments where
nonlinear effects are negligible (abridged).

23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin