Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Connectivity properties of the adjacency graph of SLE$_\kappa$ bubbles
  for $\kappa \in (4,8)$   We study the adjacency graph of bubbles---i.e., complementary connected
components---of an SLE$_{\kappa}$ curve for $\kappa \in (4,8)$, with two such
bubbles considered to be adjacent if their boundaries intersect. We show that
this adjacency graph is a.s. connected for $\kappa \in (4,\kappa_0]$, where
$\kappa_0 \approx 5.6158$ is defined explicitly. This gives a partial answer to
a problem posed by Duplantier, Miller and Sheffield (2014). Our proof in fact
yields a stronger connectivity result for $\kappa \in (4,\kappa_0]$, which says
that there is a Markovian way of finding a path from any fixed bubble to
$\infty$. We also show that there is a (non-explicit) $\kappa_1 \in (\kappa_0,
8)$ such that this stronger condition does not hold for $\kappa \in
[\kappa_1,8)$.
  Our proofs are based on an encoding of SLE$_\kappa$ in terms of a pair of
independent $\kappa/4$-stable processes, which allows us to reduce our problem
to a problem about stable processes. In fact, due to this encoding, our results
can be re-phrased as statements about the connectivity of the adjacency graph
of loops when one glues together an independent pair of so-called
$\kappa/4$-stable looptrees, as studied, e.g., by Curien and Kortchemski
(2014).
  The above encoding comes from the theory of Liouville quantum gravity (LQG),
but the paper can be read without any knowledge of LQG if one takes the
encoding as a black box.

25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat