Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The skew Brownian permuton: a new universality class for random
  constrained permutations   We construct a new family of random permutons, called skew Brownian permuton,
which describes the limits of various models of random constrained
permutations. This family is parametrized by two real parameters.
  For a specific choice of the parameters, the skew Brownian permuton coincides
with the Baxter permuton, i.e. the permuton limit of Baxter permutations. We
prove that for another specific choice of the parameters, the skew Brownian
permuton coincides with the biased Brownian separable permuton, a one-parameter
family of permutons previously studied in the literature as limit of uniform
permutations in substitution-closed classes. This brings two different limiting
objects under the same roof, identifying a new larger universality class.
  The skew Brownian permuton is constructed in terms of some stochastic
differential equations (SDEs) driven by two-dimensional correlated Brownian
excursions in the non-negative quadrant. We call these SDEs skew perturbed
Tanaka equations because they are a mixture of the perturbed Tanaka equations
and the equations encoding skew Brownian motions. We prove existence and
uniqueness of (strong) solutions for these new SDEs.
  In addition, we show that some natural permutons arising from SLE-decorated
Liouville quantum spheres are skew Brownian permutons and such permutons cover
almost the whole range of possible parameters. The connection between models of
constrained permutations and models of decorated planar maps has been
intensively investigated in the literature at the discrete level; this paper
establishes this connection directly at the continuum level. Proving the latter
result, we also give an SDE interpretation of some quantities related to
SLE-decorated Liouville quantum spheres.
  We finally collect a series of intriguing open-questions on these new
limiting permutons.

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The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
5
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: nlin
8
The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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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: quant-ph
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The categories of this paper are: nucl-th