Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractional $P(\phi)_1$-processes and Gibbs measures   We define and prove existence of fractional $P(\phi)_1$-processes as random
processes generated by fractional Schr\"odinger semigroups with
Kato-decomposable potentials. Also, we show that the measure of such a process
is a Gibbs measure with respect to the same potential. We give conditions of
its uniqueness and characterize its support relating this with intrinsic
ultracontractivity properties of the semigroup and the fall-off of the ground
state. To achieve that we establish and analyze these properties first.

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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: eess
6
The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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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: alg-geom
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The categories of this paper are: comp-gas