Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Divide and color representations for threshold Gaussian and stable
  vectors   We study the question of when a (\{0,1\})-valued threshold process associated
to a mean zero Gaussian or a symmetric stable vector corresponds to a {\it
divide and color (DC) process}. This means that the process corresponding to
fixing a threshold level $h$ and letting a 1 correspond to the variable being
larger than $h$ arises from a random partition of the index set followed by
coloring {\it all} elements in each partition element 1 or 0 with probabilities
$p$ and $1-p$, independently for different partition elements.
  While it turns out that all discrete Gaussian free fields yield a DC process
when the threshold is zero, for general $n$-dimensional mean zero, variance one
Gaussian vectors with nonnegative covariances, this is true in general when
$n=3$ but is false for $n=4$.
  The behavior is quite different depending on whether the threshold level $h$
is zero or not and we show that there is no general monotonicity in $h$ in
either direction. We also show that all constant variance discrete Gaussian
free fields with a finite number of variables yield DC processes for large
thresholds.
  In the stable case, for the simplest nontrivial symmetric stable vector with
three variables, we obtain a phase transition in the stability exponent
$\alpha$ at the surprising value of $1/2$; if the index of stability is larger
than $1/2$, then the process yields a DC process for large $h$ while if the
index of stability is smaller than $1/2$, then this is not the case.

33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con