{"id":184875,"date":"2010-05-07T00:00:00","date_gmt":"2010-05-14T20:29:54","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/width-and-height-of-conditioned-galton-watson-trees\/"},"modified":"2016-08-22T11:27:23","modified_gmt":"2016-08-22T18:27:23","slug":"width-and-height-of-conditioned-galton-watson-trees","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/width-and-height-of-conditioned-galton-watson-trees\/","title":{"rendered":"Width and height of conditioned Galton-Watson trees"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Consider a random Galton-Watson tree conditioned to have size n.<br \/>\nWe assume that the offspring distribution has mean 1 and finite variance, but no further moment conditions.<br \/>\nIt is well-known that the width and height both are of the order n<sup>1\/2<\/sup> (see for example Aldous (1991) for much more detailed results on the shape). I will talk about about proving tail estimates, for example P(width > k) < exp(-c k<sup>2<\/sup>\/n). (Note that no such exponential tail bounds are assumed for the offspring distribution.) The proof uses a finite version of the size-biazed Galton-Watson tree studied by Lyons, Pemantle and Peres (1995).<br \/>\n(Joint work with Louigi Addario-Berry and Luc Devroye.)<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Consider a random Galton-Watson tree conditioned to have size n. We assume that the offspring distribution has mean 1 and finite variance, but no further moment conditions. It is well-known that the width and height both are of the order n1\/2 (see for example Aldous (1991) for much more detailed results on the shape). I [&hellip;]<\/p>\n","protected":false},"featured_media":195624,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":0,"footnotes":""},"research-area":[],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-184875","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/ypKkCcjviNA","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/184875","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/184875\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/195624"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=184875"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=184875"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=184875"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=184875"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=184875"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=184875"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=184875"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=184875"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=184875"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=184875"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}