{"id":190041,"date":"2013-10-20T00:00:00","date_gmt":"2013-10-22T18:07:07","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/a-two-sided-estimate-for-the-gaussian-noise-stability-deficit\/"},"modified":"2016-08-10T07:17:28","modified_gmt":"2016-08-10T14:17:28","slug":"a-two-sided-estimate-for-the-gaussian-noise-stability-deficit","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/a-two-sided-estimate-for-the-gaussian-noise-stability-deficit\/","title":{"rendered":"A Two-Sided Estimate for the Gaussian Noise Stability Deficit"},"content":{"rendered":"<div class=\"asset-content\">\n<p>The Gaussian Noise Stability of a set A in Euclidean space is the probability that for a Gaussian vector X conditioned to be in A, a small Gaussian perturbation of X will also be in A. Borel&#8217;s celebrated Isoperimetric inequality states that a half-space maximizes noise stability among sets with the same Gaussian measure. We will present a novel short proof of this inequality, based on stochastic calculus. Moreover, we prove an almost tight, two-sided, dimension-free robustness estimate for this inequality: We show that the deficit between the noise stability of a set A and an equally probable half-space H can be controlled by a function of the distance between the corresponding centroids. As a consequence, we prove a conjecture by Mossel and Neeman, who used the total-variation distance.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Gaussian Noise Stability of a set A in Euclidean space is the probability that for a Gaussian vector X conditioned to be in A, a small Gaussian perturbation of X will also be in A. Borel&#8217;s celebrated Isoperimetric inequality states that a half-space maximizes noise stability among sets with the same Gaussian measure. We [&hellip;]<\/p>\n","protected":false},"featured_media":197941,"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-190041","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/_j4pU4HQGGk","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/190041","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\/190041\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/197941"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=190041"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=190041"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=190041"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=190041"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=190041"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=190041"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=190041"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=190041"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=190041"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=190041"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}