Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hypergeometric SLE: Conformal Markov Characterization and Applications   This article pertains to the classification of pairs of simple random curves
with conformal Markov property and symmetry. We give the complete
classification of such curves: conformal Markov property and symmetry single
out a two-parameter family of random curves---Hypergeometric SLE---denoted by
hSLE$_{\kappa}(\nu)$ for $\kappa\in (0,4]$ and $\nu<\kappa-6$. The proof relies
crucially on Dub\'edat's commutation relation [Dub07] and a uniqueness result
proved in [MS16b]. The classification indicates that hypergeometric SLE is the
only possible scaling limit of the interfaces in critical lattice models
(conjectured or proved to be conformal invariant) in topological rectangles
with alternating boundary conditions.
  We also prove various properties of hSLE: continuity, reversibility,
target-independence, and conditional law characterization. As by-products, we
give two applications of these properties. The first one is about the critical
Ising interfaces. We prove the convergence of the Ising interface in rectangles
with alternating boundary conditions. This result was first proved by Izyurov
in [Izy15], but our proof is new which is based on the properties of hSLE. The
second application is the existence of the so-called pure partition functions
of multiple SLEs. Such existence was proved for $\kappa\in (0,8)\setminus
\mathbb{Q}$ in [KP16], and it was later proved for $\kappa\in (0,4]$ in [PW17].
We give a new proof of the existence for $\kappa\in (0,6]$ using the properties
of hSLE.

6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
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The categories of this paper are: econ
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
29
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: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga