Logarithmic inequalities under a symmetric polynomial dominance order
Name
S0002-9939-2018-14023-X.pdf
Description
Published version
Size
158.39 KB
Format
Unknown
Checksum (MD5)
526012337d84328dcea1066158a04978
Author(s)
Sra, Suvrit
Date Issued
2018
Journal
Proceedings of the American Mathematical Society
Publisher
American Mathematical Society (AMS)
Version
Final published version
Abstract
© 2018 American Mathematical Society. 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 “sum-of-squared-logarithms” inequality conjectured in (Bîrsan, Neff, and Lankeit, J. Inequalities and Applications (2013); P. Neff, Y. Nakatsukasa, and A. Fischle; 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 Rényi entropy, subentropy, and quantum Rényi entropy.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1090/PROC/14023
