Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Lundh's percolation difussion   A collection of spherical obstacles in the ball in Euclidean space is said to
be avoidable for Brownian motion if there is a positive probability that
Brownian motion diffusing from some point in the ball will avoid all the
obstacles and reach the boundary of the ball. The centres of the spherical
obstacles are generated according to a Poisson point process while the radius
of an obstacle is a deterministic function depending only on the distance from
the obstacle's centre to the centre of the ball. Lundh has given the name
percolation diffusion to this process if avoidable configurations are generated
with positive probability. An integral condition for percolation diffusion is
derived in terms of the intensity of the Poisson point process and the function
that determines the radii of the obstacles.

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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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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: gr-qc
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex