{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:13:49Z","timestamp":1758824029480},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2017,3,29]],"date-time":"2017-03-29T00:00:00Z","timestamp":1490745600000},"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":[[2017,5]]},"abstract":"<jats:p>We prove an inequality for functions on the discrete cube {0, 1}<jats:sup><jats:italic>n<\/jats:italic><\/jats:sup> extending the edge-isoperimetric inequality for sets. This inequality turns out to be equivalent to the following claim about random walks on the cube: subcubes maximize \u2018mean first exit time\u2019 among all subsets of the cube of the same cardinality.<\/jats:p>","DOI":"10.1017\/s0963548316000432","type":"journal-article","created":{"date-parts":[[2017,3,29]],"date-time":"2017-03-29T02:48:55Z","timestamp":1490755735000},"page":"468-480","source":"Crossref","is-referenced-by-count":4,"title":["An Inequality for Functions on the Hamming Cube"],"prefix":"10.1017","volume":"26","author":[{"given":"ALEX","family":"SAMORODNITSKY","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2017,3,29]]},"reference":[{"key":"S0963548316000432_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548306008340"},{"key":"S0963548316000432_ref4","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548311000083"},{"key":"S0963548316000432_ref12","unstructured":"Ros A. (2001) The isoperimetric problem. http:\/\/www.ugr.es\/~aros\/isoper.htm"},{"key":"S0963548316000432_ref11","volume-title":"Foundations and Trends in Theoretical Computer Science","author":"Montenegro","year":"2005"},{"key":"S0963548316000432_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2008.03.023"},{"key":"S0963548316000432_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8005-3"},{"key":"S0963548316000432_ref2","unstructured":"Bezrukov S. (1994) Isoperimetric problems in discrete spaces. In Extremal Problems for Finite Sets ( P. Frankl , Z. F\u00fcredi , G. Katona and D. Miklos , eds), Vol. 3 of Bolyai Society Mathematical Studies, pp. 59\u201391."},{"key":"S0963548316000432_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s00039-002-8235-y"},{"key":"S0963548316000432_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(66)80059-5"},{"key":"S0963548316000432_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s004930070011"},{"key":"S0963548316000432_ref3","volume-title":"Combinatorics: Set Systems, Hypergraphs, Families of Vectors, and Combinatorial Probability","author":"Bollobas","year":"1986"},{"key":"S0963548316000432_ref7","doi-asserted-by":"publisher","DOI":"10.2307\/2373688"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548316000432","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T19:01:13Z","timestamp":1555527673000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548316000432\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,29]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,5]]}},"alternative-id":["S0963548316000432"],"URL":"https:\/\/doi.org\/10.1017\/s0963548316000432","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,29]]}}}