Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The universality classes in the parabolic Anderson model   We discuss the long time behaviour of the parabolic Anderson model, the
Cauchy problem for the heat equation with random potential on $\Z^d$. We
consider general i.i.d. potentials and show that exactly \emph{four}
qualitatively different types of intermittent behaviour can occur. These four
universality classes depend on the upper tail of the potential distribution:
(1) tails at $\infty$ that are thicker than the double-exponential tails, (2)
double-exponential tails at $\infty$ studied by G\"artner and Molchanov, (3) a
new class called \emph{almost bounded potentials}, and (4) potentials bounded
from above studied by Biskup and K\"onig. The new class (3), which contains
both unbounded and bounded potentials, is studied in both the annealed and the
quenched setting. We show that intermittency occurs on unboundedly increasing
islands whose diameter is slowly varying in time. The characteristic
variational formulas describing the optimal profiles of the potential and of
the solution are solved explicitly by parabolas, respectively, Gaussian
densities.

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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ