Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poincare Inequality on the Path Space of Poisson Point Processes   The quasi-invariance is proved for the distributions of Poisson point
processes under a random shift map on the path space. This leads to a natural
Dirichlet form of jump type on the path space. Differently from the O-U
Dirichlet form on the Wiener space satisfying the log-Sobolev inequality, this
Dirichlet form merely satisfies the Poincare inequality but not the log-Sobolev
one.

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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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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: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph