Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phi-Entropic Measures of Correlation   A measure of correlation is said to have the tensorization property if it is
unchanged when computed for i.i.d.\ copies. More precisely, a measure of
correlation between two random variables $(X, Y)$ denoted by $\rho(X, Y)$, has
the tensorization property if $\rho(X^n, Y^n)=\rho(X, Y)$ where $(X^n, Y^n)$ is
$n$ i.i.d.\ copies of $(X, Y)$.Two well-known examples of such measures are the
maximal correlation and the hypercontractivity ribbon (HC~ribbon). We show that
the maximal correlation and HC ribbons are special cases of $\Phi$-ribbon,
defined in this paper for any function $\Phi$ from a class of convex functions
($\Phi$-ribbon reduces to HC~ribbon and the maximal correlation for special
choices of $\Phi$). Any $\Phi$-ribbon is shown to be a measures of correlation
with the tensorization property. We show that the $\Phi$-ribbon also
characterizes the $\Phi$-strong data processing inequality constant introduced
by Raginsky. We further study the $\Phi$-ribbon for the choice of $\Phi(t)=t^2$
and introduce an equivalent characterization of this ribbon.

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The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
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The categories of this paper are: eess
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th