Logarithmic inequalities under a symmetric polynomial dominance order
© 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...
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| Format: | Article |
| Language: | English |
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American Mathematical Society (AMS)
2021
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| Online Access: | https://hdl.handle.net/1721.1/135168.2 |
| _version_ | 1811089911532486656 |
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| author | Sra, Suvrit |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Sra, Suvrit |
| author_sort | Sra, Suvrit |
| collection | MIT |
| description | © 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. |
| first_indexed | 2024-09-23T14:27:20Z |
| format | Article |
| id | mit-1721.1/135168.2 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:27:20Z |
| publishDate | 2021 |
| publisher | American Mathematical Society (AMS) |
| record_format | dspace |
| spelling | mit-1721.1/135168.22021-11-29T14:05:29Z Logarithmic inequalities under a symmetric polynomial dominance order Sra, Suvrit Massachusetts Institute of Technology. Department of Mathematics © 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. 2021-11-29T14:05:28Z 2021-10-27T20:11:04Z 2021-11-29T14:05:28Z 2018 2021-03-30T13:59:39Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/135168.2 en 10.1090/PROC/14023 Proceedings of the American Mathematical Society 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. application/octet-stream American Mathematical Society (AMS) American Mathematical Society |
| spellingShingle | Sra, Suvrit Logarithmic inequalities under a symmetric polynomial dominance order |
| title | Logarithmic inequalities under a symmetric polynomial dominance order |
| title_full | Logarithmic inequalities under a symmetric polynomial dominance order |
| title_fullStr | Logarithmic inequalities under a symmetric polynomial dominance order |
| title_full_unstemmed | Logarithmic inequalities under a symmetric polynomial dominance order |
| title_short | Logarithmic inequalities under a symmetric polynomial dominance order |
| title_sort | logarithmic inequalities under a symmetric polynomial dominance order |
| url | https://hdl.handle.net/1721.1/135168.2 |
| work_keys_str_mv | AT srasuvrit logarithmicinequalitiesunderasymmetricpolynomialdominanceorder |