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Logarithmic inequalities under an elementary symmetric polynomial dominance order. (arXiv:1509.05902v2 [math.CA] UPDATED)
来源于:arXiv
We consider a dominance order on positive vectors induced by the elementary
symmetric polynomials. Under this dominance order we provide conditions that
yield simple proofs of several monotonicity questions. Notably, our approach
yields a quick (4 line) proof of the so-called
\emph{"sum-of-squared-logarithms"} inequality conjectured in (P.~Neff,
B.~Eidel, F.~Osterbrink, and R.~Martin, \emph{Applied Math. \& Mechanics.,
2013}; P.~Neff, Y.~Nakatsukasa, and A.~Fischle; \emph{SIMAX, 35, 2014}). This
inequality has been the subject of several recent articles, and only recently
it received a full proof, albeit via a more elaborate complex-analytic
approach. We provide an elementary proof, which moreover extends to yield
simple proofs of both old and new inequalities for R\'enyi entropy, subentropy,
and quantum R\'enyi entropy. 查看全文>>