Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean conservation of nodal volume and connectivity measures for Gaussian
  ensembles   We study in depth the nesting graph and volume distribution of the nodal
domains of a Gaussian field, which have been shown in previous works to exhibit
asymptotic laws. A striking link is established between the asymptotic mean
connectivity of a nodal domain (i.e.\ the vertex degree in its nesting graph)
and the positivity of the percolation probability of the field, along with a
direct dependence of the average nodal volume on the percolation probability.
Our results support the prevailing ansatz that the mean connectivity and volume
of a nodal domain is conserved for generic random fields in dimension $d=2$ but
not in $d \ge 3$, and are applied to a number of concrete motivating examples.

8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin