Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zero entropy is generic   Dan Rudolph showed that for an amenable group $\Gamma$, the generic
measure-preserving action of $\Gamma$ on a Lebesgue space has zero entropy.
Here this is extended to nonamenable groups. In fact, the proof shows that
every action is a factor of a zero entropy action! This uses the strange
phenomena that in the presence of nonamenability, entropy can increase under a
factor map. The proof uses Seward's recent generalization of Sinai's Factor
Theorem, the Gaboriau-Lyons result and my theorem that for every nonabelian
free group, all Bernoulli shifts factor onto each other.

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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph