Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean density of inhomogeneous Boolean models with lower dimensional
  typical grain   The mean density of a random closed set $\Theta$ in $\R^d$ with Hausdorff
dimension $n$ is the Radon-Nikodym derivative of the expected measure
$\E[\h^n(\Theta\cap\cdot)]$ induced by $\Theta$ with respect to the usual
$d$-dimensional Lebesgue measure. We consider here inhomogeneous Boolean models
with lower dimensional typical grain. Under general regularity assumptions on
the typical grain, related to the existence of its Minkowski content, and on
the intensity measure of the underlying Poisson point process, we prove an
explicit formula for the mean density. The proof of such formula provides as
by-product estimators for the mean density in terms of the empirical capacity
functional, which turns to be closely related to the well known random variable
density estimation by histograms in the extreme case $n=0$. Particular cases
and examples are also discussed.

34
The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
1
The categories of this paper are: cs
16
The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
9
The categories of this paper are: nlin