{"id":3141,"date":"2021-10-21T15:53:20","date_gmt":"2021-10-21T19:53:20","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/boyland\/?page_id=3141"},"modified":"2026-03-19T08:10:24","modified_gmt":"2026-03-19T12:10:24","slug":"james-melbourne","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/boyland\/james-melbourne\/","title":{"rendered":"James Melbourne"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<h1 class=\"wp-block-heading\">James Melbourne<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">\u00a0Majorization: in information theory, analysis, and beyond.<\/h3>\n\n\n\n<p>Abstract: Modulo permutations, the notion of majorization gives a useful partial order on the set of n-dimension probability vectors. Classically in probability and information theory, the R\\&#8217;enyi entropy reverses this ordering, a property referred to as Schur-concavity. We will explore the notion of majorization for proving analytic inequalities. In particular we present a transportation argument that yields a majorizing relationship between densities. As applications, elementary derivations of certain Fourier theoretic L^p norm comparisons can be obtained. Time permitting, we will discuss geometric and combinatorial consequences of the obtained bounds.<\/p>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":146,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-3141","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/3141","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/users\/146"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/comments?post=3141"}],"version-history":[{"count":2,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/3141\/revisions"}],"predecessor-version":[{"id":3854,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/3141\/revisions\/3854"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/media?parent=3141"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}