Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bernoulli Correlations and Cut Polytopes   Given $n$ symmetric Bernoulli variables, what can be said about their
correlation matrix viewed as a vector? We show that the set of those vectors
$R(\mathcal{B}_n)$ is a polytope and identify its vertices. Those extreme
points correspond to correlation vectors associated to the discrete uniform
distributions on diagonals of the cube $[0,1]^n$. We also show that the
polytope is affinely isomorphic to a well-known cut polytope ${\rm CUT}(n)$
which is defined as a convex hull of the cut vectors in a complete graph with
vertex set $\{1,\ldots,n\}$. The isomorphism is obtained explicitly as
$R(\mathcal{B}_n)= {\mathbf{1}}-2~{\rm CUT}(n)$. As a corollary of this work,
it is straightforward using linear programming to determine if a particular
correlation matrix is realizable or not. Furthermore, a sampling method for
multivariate symmetric Bernoullis with given correlation is obtained. In some
cases the method can also be used for general, not exclusively Bernoulli,
marginals.

30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th