Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conformal Loop Ensembles: The Markovian characterization and the
  loop-soup construction   For random collections of self-avoiding loops in two-dimensional domains, we
define a simple and natural conformal restriction property that is
conjecturally satisfied by the scaling limits of interfaces in models from
statistical physics. This property is basically the combination of conformal
invariance and the locality of the interaction in the model. Unlike the Markov
property that Schramm used to characterize SLE curves (which involves
conditioning on partially generated interfaces up to arbitrary stopping times),
this property only involves conditioning on entire loops and thus appears at
first glance to be weaker.
  Our first main result is that there exists exactly a one-dimensional family
of random loop collections with this property---one for each k in (8/3,4]---and
that the loops are forms of SLE(k). The proof proceeds in two steps. First,
uniqueness is established by showing that every such loop ensemble can be
generated by an "exploration" process based on SLE.
  Second, existence is obtained using the two-dimensional Brownian loop-soup,
which is a Poissonian random collection of loops in a planar domain. When the
intensity parameter c of the loop-soup is less than 1, we show that the outer
boundaries of the loop clusters are disjoint simple loops (when c>1 there is
almost surely only one cluster) that satisfy the conformal restriction axioms.
We prove various results about loop-soups, cluster sizes, and the c=1 phase
transition.
  Taken together, our results imply that the following families are equivalent:
  1. The random loop ensembles traced by certain branching SLE(k) curves for k
in (8/3, 4].
  2. The outer-cluster-boundary ensembles of Brownian loop-soups for c in (0,
1].
  3. The (only) random loop ensembles satisfying the conformal restriction
axioms.

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The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th