{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,8,16]],"date-time":"2022-08-16T20:12:55Z","timestamp":1660680775678},"reference-count":24,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2018,3,23]],"date-time":"2018-03-23T00:00:00Z","timestamp":1521763200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2018,5]]},"abstract":"<jats:p>Keller and Kindler recently established a quantitative version of the famous Benjamini\u2013Kalai\u2013Schramm theorem on the noise sensitivity of Boolean functions. Their result was extended to the continuous Gaussian setting by Keller, Mossel and Sen by means of a Central Limit Theorem argument. In this work we present a unified approach to these results, in both discrete and continuous settings. The proof relies on semigroup decompositions together with a suitable cut-off argument, allowing for the efficient use of the classical hypercontractivity tool behind these results. It extends to further models of interest such as families of log-concave measures and Cayley and Schreier graphs. In particular we obtain a quantitative version of the Benjamini\u2013Kalai\u2013Schramm theorem for the slices of the Boolean cube.<\/jats:p>","DOI":"10.1017\/s0963548318000044","type":"journal-article","created":{"date-parts":[[2018,3,23]],"date-time":"2018-03-23T07:03:11Z","timestamp":1521788591000},"page":"334-357","source":"Crossref","is-referenced-by-count":2,"title":["On Quantitative Noise Stability and Influences for Discrete and Continuous Models"],"prefix":"10.1017","volume":"27","author":[{"given":"RAPHA\u00cbL","family":"BOUYRIE","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,3,23]]},"reference":[{"key":"S0963548318000044_ref24","doi-asserted-by":"publisher","DOI":"10.1007\/BF01200910"},{"key":"S0963548318000044_ref21","doi-asserted-by":"publisher","DOI":"10.1137\/100787325"},{"key":"S0963548318000044_ref18","doi-asserted-by":"crossref","first-page":"1855","DOI":"10.1214\/aop\/1022855885","article-title":"Logarithmic Sobolev inequality for some models of random walks.","volume":"26","author":"Lee","year":"1998","journal-title":"Ann. Probab."},{"key":"S0963548318000044_ref13","first-page":"25","volume-title":"Computational Complexity and Statistical Physics","author":"Kalai","year":"2006"},{"key":"S0963548318000044_ref12","doi-asserted-by":"publisher","DOI":"10.2307\/2373688"},{"key":"S0963548318000044_ref11","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139924160","volume-title":"Lectures on Noise Sensitivity and Percolation","author":"Garban","year":"2014"},{"key":"S0963548318000044_ref9","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1214\/aoap\/1034968224","article-title":"Logarithmic Sobolev inequalities for finite Markov chains.","volume":"6","author":"Diaconis","year":"1996","journal-title":"Ann. Appl. Probab."},{"key":"S0963548318000044_ref5","doi-asserted-by":"publisher","DOI":"10.2307\/1970980"},{"key":"S0963548318000044_ref1","volume-title":"Sur les In\u00e9galit\u00e9s de Sobolev Logarithmiques","author":"An\u00e9","year":"2000"},{"key":"S0963548318000044_ref23","doi-asserted-by":"publisher","DOI":"10.1007\/BF01844850"},{"key":"S0963548318000044_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02698830"},{"key":"S0963548318000044_ref19","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0119290"},{"key":"S0963548318000044_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0073871"},{"key":"S0963548318000044_ref17","doi-asserted-by":"publisher","DOI":"10.5802\/afst.962"},{"key":"S0963548318000044_ref3","first-page":"177","volume-title":"S\u00e9minaire de Probabilit\u00e9s XIX","author":"Bakry","year":"1985"},{"key":"S0963548318000044_ref10","unstructured":"Forsstr\u00f6m M. P. (2015) A noise sensitivity theorem for Schreier graphs. arXiv:1501.01828"},{"key":"S0963548318000044_ref22","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176988612"},{"key":"S0963548318000044_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-013-2719-2"},{"key":"S0963548318000044_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-00227-9"},{"key":"S0963548318000044_ref7","doi-asserted-by":"publisher","DOI":"10.5802\/aif.357"},{"key":"S0963548318000044_ref15","doi-asserted-by":"publisher","DOI":"10.1214\/11-AOP643"},{"key":"S0963548318000044_ref16","doi-asserted-by":"publisher","DOI":"10.1214\/13-AIHP557"},{"key":"S0963548318000044_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-29849-3_10"},{"key":"S0963548318000044_ref20","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(73)90025-6"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548318000044","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,16]],"date-time":"2022-08-16T19:57:22Z","timestamp":1660679842000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548318000044\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,23]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,5]]}},"alternative-id":["S0963548318000044"],"URL":"https:\/\/doi.org\/10.1017\/s0963548318000044","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,23]]}}}