{"id":513,"date":"2016-06-02T09:01:47","date_gmt":"2016-06-02T06:01:47","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=513"},"modified":"2016-06-10T11:04:28","modified_gmt":"2016-06-10T08:04:28","slug":"colloquium-tuesday-june-7-2-pm-speaker-jonathan-aaronson-tel-aviv-title-distributional-limits-of-positive-ergodic-stationary-processes-infinite-ergodic-transformations","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=513","title":{"rendered":"Colloquium: Tuesday, June 7, 2 pm. Speaker: Jonathan Aaronson (Tel Aviv). Title: &#8220;Distributional limits of positive, ergodic stationary processes &#038; infinite ergodic transformations&#8221;."},"content":{"rendered":"<div dir=\"ltr\">\n<div class=\"gmail_default\">In infinite ergodic theory, distributional limits replace the absolutely normalized pointwise ergodic theorem.We&#8217;ll review the subject and then see that every random variable on the positive reals occurs as the distributional limit of some infinite ergodic transformation.<\/p>\n<p>We&#8217;ll consider consequences in infinite ergodic theory: e.g. rational ergodicity properties.<\/p>\n<p>It follows from a duality technique (&#8220;inversion&#8221;) that every random variable on the positive reals occurs as the distributional limit of the partial sums of some positive, ergodic stationary process\u00a0 normalized by a 1-regularly varying normalizing sequence (&amp; the process can be chosen\u00a0over any EPPT).<\/p>\n<p>arXiv:1604.03218<\/p>\n<\/div>\n<div class=\"gmail_default\">Joint work with Benjamin Weiss<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>In infinite ergodic theory, distributional limits replace the absolutely normalized pointwise ergodic theorem.We&#8217;ll review the subject and then see that every random variable on the positive reals occurs as the distributional limit of some infinite ergodic transformation. We&#8217;ll consider consequences&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=513\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-513","post","type-post","status-publish","format-standard","hentry","category-colloquium"],"_links":{"self":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/513","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=513"}],"version-history":[{"count":2,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/513\/revisions"}],"predecessor-version":[{"id":531,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/513\/revisions\/531"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=513"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=513"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=513"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}