Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conditioning a Brownian loop-soup cluster on a portion of its boundary   We show that if one conditions a cluster in a Brownian loop-soup $L$ (of any
intensity) in a two-dimensional domain by a portion $l$ of its outer boundary,
then in the remaining domain, the union of all the loops of $L$ that touch $l$
satisfies the conformal restriction property while the other loops in $L$ form
an independent loop-soup. This result holds when one discovers $l$ in a natural
Markovian way, such as in the exploration procedures that have been defined in
order to actually construct the Conformal Loop Ensembles as outer boundaries of
loop-soup clusters. This result implies among other things that a phase
transition occurs at c = 14/15 for the connectedness of the loops that touch
$l$.
  Our results can be viewed as an extension of some of the results in our
earlier paper in the following two directions: There, a loop-soup cluster was
conditioned on its entire outer boundary while we discover here only part of
this boundary. And, while it was explained there that the strong decomposition
using a Poisson point process of excursions that we derived there should be
specific to the case of the critical loop-soup, we show here that in the
subcritical cases, a weaker property involving the conformal restriction
property nevertheless holds.

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The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: cs