{"id":3059,"date":"2025-10-28T13:56:17","date_gmt":"2025-10-28T16:56:17","guid":{"rendered":"https:\/\/icc.fcen.uba.ar\/?p=3059"},"modified":"2025-10-28T13:57:00","modified_gmt":"2025-10-28T16:57:00","slug":"rauzy-complexity-and-block-entropy","status":"publish","type":"post","link":"https:\/\/icc.fcen.uba.ar\/en\/rauzy-complexity-and-block-entropy\/","title":{"rendered":"Rauzy complexity and block entropy"},"content":{"rendered":"<div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 fusion-flex-container has-pattern-background has-mask-background nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1144px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-0 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-text fusion-text-1\"><p>Authors: Ver\u00f3nica Becher; Olivier Carton; Santiago Figueira.<\/p>\n<p>Abstract:<br \/>\nIn 1976, Rauzy studied two complexity functions, \u03b2 and \u03b2, for infinite sequences over a finite alphabet. The function \u03b2 achieves its maximum precisely for Borel normal sequences,<br \/>\nwhile \u03b2 reaches its minimum for sequences that, when added to any Borel normal sequence, result in another Borel normal sequence. We establish a connection between Rauzy\u2019s complexity functions, \u03b2 and \u03b2, and the notions of non-aligned block entropy, h and h, by providing sharp upper and lower bounds for h in terms of \u03b2, and sharp upper and lower bounds for h in terms of \u03b2. We adopt a probabilistic approach by considering an infinite sequence of random variables over a finite alphabet. The proof relies on a new characterization of non-aligned<br \/>\nblock entropies, h and h, in terms of Shannon\u2019s conditional entropy. The bounds imply that sequences with h = 0 coincide with those for which \u03b2 = 0. We also show that the non-aligned block entropies, h and h, are essentially subadditive.<\/p>\n<p>More information:<br \/>\n<a href=\"https:\/\/arxiv.org\/html\/2406.18383v2\" target=\"_blank\" rel=\"noopener\">https:\/\/arxiv.org\/html\/2406.18383v2<\/a><\/p>\n<\/div><\/div><\/div><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":9,"featured_media":3061,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[98],"tags":[],"class_list":["post-3059","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-papers"],"_links":{"self":[{"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/posts\/3059","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/comments?post=3059"}],"version-history":[{"count":2,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/posts\/3059\/revisions"}],"predecessor-version":[{"id":3062,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/posts\/3059\/revisions\/3062"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/media\/3061"}],"wp:attachment":[{"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/media?parent=3059"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/categories?post=3059"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/tags?post=3059"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}