{"id":191308,"date":"2014-08-13T00:00:00","date_gmt":"2014-08-13T16:32:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/talagrands-convolution-conjecture\/"},"modified":"2016-07-15T15:19:04","modified_gmt":"2016-07-15T22:19:04","slug":"talagrands-convolution-conjecture","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/talagrands-convolution-conjecture\/","title":{"rendered":"Talagrand&#8217;s Convolution Conjecture"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Tools from James Lee\u2019s July 28 talk will be employed to prove the following: Any non-negative function f on Gaussian space that is not too log-concave has tails strictly better than those given by Markov&#8217;s inequality:  P(f > c) < E[f]\/(c (log c)<sup>1\/6<\/sup>) where E[f] denotes the (Gaussian) expectation of f.  An immediate consequence is a positive answer to Talagrand&#8217;s (1989) question about regularization of L<sup>1<\/sup> functions under convolution.  (Joint work with James Lee).<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tools from James Lee\u2019s July 28 talk will be employed to prove the following: Any non-negative function f on Gaussian space that is not too log-concave has tails strictly better than those given by Markov&#8217;s inequality: P(f > c) < E[f]\/(c (log c)1\/6) where E[f] denotes the (Gaussian) expectation of f. An immediate consequence is [&hellip;]\n<\/p>\n","protected":false},"featured_media":198565,"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":[206954],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-191308","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-video-type-microsoft-research-talks","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/6VsYMF05n5Y","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/191308","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\/191308\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/198565"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=191308"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=191308"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=191308"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=191308"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=191308"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=191308"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=191308"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=191308"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=191308"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=191308"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}