{"id":2332,"date":"2022-05-27T13:25:12","date_gmt":"2022-05-27T16:25:12","guid":{"rendered":"https:\/\/icc.fcen.uba.ar\/?p=2332"},"modified":"2022-05-27T13:25:12","modified_gmt":"2022-05-27T16:25:12","slug":"randomness-and-uniform-distribution-modulo-one","status":"publish","type":"post","link":"https:\/\/icc.fcen.uba.ar\/en\/randomness-and-uniform-distribution-modulo-one\/","title":{"rendered":"Randomness and uniform distribution modulo one"},"content":{"rendered":"<div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 fusion-flex-container 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, Serge Grigorieff.<\/p>\n<p>Abstract:<\/p>\n<p>We elaborate the notions of Martin-L\u00f6f and Schnorr randomness for real numbers in terms of uniform distribution of sequences. We give a necessary condition for a real number to be Schnorr random expressed in terms of classical uniform distribution of sequences. This extends the result proved by Avigad for sequences of linear functions with integer coefficients to the wider classical class of Koksma sequences of functions. And, by requiring equidistribution with respect to every computably enumerable open set (respectively, computably enumerable open set with computable measure) in the unit interval, we give a sufficient condition for Martin-L\u00f6f (respectively Schnorr) randomness.<\/p>\n<p>More information:<\/p>\n<p><a href=\"https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S0890540121001899\" target=\"_blank\" rel=\"noopener noreferrer\">https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S0890540121001899<\/a><\/p>\n<\/div><\/div><\/div><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":9,"featured_media":2333,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[98],"tags":[],"class_list":["post-2332","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\/2332","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=2332"}],"version-history":[{"count":1,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/posts\/2332\/revisions"}],"predecessor-version":[{"id":2334,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/posts\/2332\/revisions\/2334"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/media\/2333"}],"wp:attachment":[{"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/media?parent=2332"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/categories?post=2332"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/tags?post=2332"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}