Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random subgroups of Thompson's group $F$   We consider random subgroups of Thompson's group $F$ with respect to two
natural stratifications of the set of all $k$ generator subgroups. We find that
the isomorphism classes of subgroups which occur with positive density are not
the same for the two stratifications.
  We give the first known examples of {\em persistent} subgroups, whose
isomorphism classes occur with positive density within the set of $k$-generator
subgroups, for all sufficiently large $k$. Additionally, Thompson's group
provides the first example of a group without a generic isomorphism class of
subgroup. Elements of $F$ are represented uniquely by reduced pairs of finite
rooted binary trees.
  We compute the asymptotic growth rate and a generating function for the
number of reduced pairs of trees, which we show is D-finite and not algebraic.
We then use the asymptotic growth to prove our density results.

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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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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: math-ph
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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: eess
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex