Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The perimeter cascade in critical Boltzmann quadrangulations decorated
  by an $O(n)$ loop model   We study the branching tree of the perimeters of the nested loops in critical
$O(n)$ model for $n \in (0,2)$ on random quadrangulations. We prove that after
renormalization it converges towards an explicit continuous multiplicative
cascade whose offspring distribution $(x_i)_{i \ge 1}$ is related to the jumps
of a spectrally positive $\alpha$-stable L\'evy process with $\alpha=
\frac{3}{2} \pm \frac{1}{\pi} \arccos(n/2)$ and for which we have the
surprisingly simple and explicit transform $$ \mathbb E\left[\sum_{i \ge 1}
(x_i)^\theta \right] = \frac{\sin(\pi (2-\alpha))}{\sin (\pi (\theta -
\alpha))} \quad \mbox{for }\theta \in (\alpha, \alpha+1).$$ An important
ingredient in the proof is a new formula of independent interest on first
moments of additive functionals of the jumps of a left-continuous random walk
stopped at a hitting time. We also identify the scaling limit of the volume of
the critical $O(n)$-decorated quadrangulation using the Malthusian martingale
associated to the continuous multiplicative cascade.

37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess