{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T16:43:16Z","timestamp":1764175396416,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T00:00:00Z","timestamp":1679616000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"publisher","award":["11688101","2018YFA0704705"],"award-info":[{"award-number":["11688101","2018YFA0704705"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"NKRDP","award":["11688101","2018YFA0704705"],"award-info":[{"award-number":["11688101","2018YFA0704705"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Recently, Ledoux, Nair, and Wang proved that the Fisher information along the heat flow is log-convex in dimension one, that is d2dt2log(I(Xt))\u22650 for n=1, where Xt is a random variable with density function satisfying the heat equation. In this paper, we consider the high dimensional case and prove that the Fisher information is square root convex in dimension two, that is d2dt2IX\u22650 for n=2. The proof is based on the semidefinite programming approach.<\/jats:p>","DOI":"10.3390\/e25040558","type":"journal-article","created":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T08:43:03Z","timestamp":1679647383000},"page":"558","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Square Root Convexity of Fisher Information along Heat Flow in Dimension Two"],"prefix":"10.3390","volume":"25","author":[{"given":"Junliang","family":"Liu","sequence":"first","affiliation":[{"name":"KLMM, UCAS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoshan","family":"Gao","sequence":"additional","affiliation":[{"name":"KLMM, UCAS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communications","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. 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