Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The geometry of random minimal factorizations of a long cycle via
  biconditioned bitype random trees   We study random typical minimal factorizations of the $n$-cycle into
transpositions, which are factorizations of $(1, \ldots,n)$ as a product of
$n-1$ transpositions. By viewing transpositions as chords of the unit disk and
by reading them one after the other, one obtains a sequence of increasing
laminations of the unit disk (i.e. compact subsets of the unit disk made of
non-intersecting chords).
  When an order of $\sqrt{n}$ consecutive transpositions have been read, we
establish, roughly speaking, that a phase transition occurs and that the
associated laminations converge to a new one-parameter family of random
laminations, constructed from excursions of specific L\'evy processes.
  Our main tools involve coding random minimal factorizations by conditioned
two-type Bienaym\'e--Galton--Watson trees. We establish in particular limit
theorems for two-type BGW trees conditioned on having given numbers of vertices
of both types, and with an offspring distribution depending on the conditioning
size. We believe that this could be of independent interest.

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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
1
The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an