Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random stable type minimal factorizations of the $n$-cycle   We investigate random minimal factorizations of the $n$-cycle, that is,
factorizations of the permutation $(1 \, 2 \cdots n)$ into a product of cycles
$\tau_1, \ldots, \tau_k$ whose lengths $\ell(\tau_1), \ldots, \ell(\tau_k)$
verify the minimality condition $\sum_{i=1}^k(\ell(\tau_i)-1)=n-1$. By
associating to a cycle of the factorization a black polygon inscribed in the
unit disk, and reading the cycles one after an other, we code a minimal
factorization by a process of colored laminations of the disk, which are
compact subsets made of red noncrossing chords delimiting faces that are either
black or white. Our main result is the convergence of this process as $n
\rightarrow \infty$, when the factorization is randomly chosen according to
Boltzmann weights in the domain of attraction of an $\alpha$-stable law, for
some $\alpha \in (1,2]$. The new limiting process interpolates between the unit
circle and a colored version of Kortchemski's $\alpha$-stable lamination. Our
principal tool in the study of this process is a bijection between minimal
factorizations and a model of size-conditioned labelled random trees whose
vertices are colored black or white.

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The categories of this paper are: eess
23
The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph