Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Excursion Set Theory of Halo Mass Functions, Halo Clustering, and
  Halo Growth   I review the excursion set theory (EST) of dark matter halo formation and
clustering. I recount the Press-Schechter argument for the mass function of
bound objects and review the derivation of the Press-Schechter mass function in
EST. The EST formalism is powerful and can be applied to numerous problems. I
review the EST of halo bias and the properties of void regions. I spend
considerable time reviewing halo growth in the EST. This section culminates
with descriptions of two Monte Carlo methods for generating halo mass accretion
histories. In the final section, I emphasize that the standard EST approach is
the result of several simplifying assumptions. Dropping these assumptions can
lead to more faithful predictions and a more versatile formalism. One such
assumption is the constant height of the barrier for nonlinear collapse. I
review implementations of the excursion set approach with arbitrary barrier
shapes. An application of this is the now well-known improvement to standard
EST that follows from the ellipsoidal-collapse barrier. Additionally, I
emphasize that the statement that halo accretion histories are independent of
halo environments is a simplifying assumption, rather than a prediction of the
theory. I review the method for constructing correlated random walks of the
density field in more general cases. I construct a simple toy model with
correlated walks and I show that excursion set theory makes a qualitatively
simple and general prediction for the relation between halo accretion histories
and halo environments: regions of high density preferentially contain
late-forming halos and conversely for regions of low density. I conclude with a
brief discussion of this prediction in the context of recent numerical studies
of the environmental dependence of halo properties. (Abridged)

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The categories of this paper are: patt-sol
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an