{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,23]],"date-time":"2024-02-23T11:49:06Z","timestamp":1708688946576},"reference-count":32,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2017,8,1]],"date-time":"2017-08-01T00:00:00Z","timestamp":1501545600000},"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":[[2018,1]]},"abstract":"<jats:p>We study factor of i.i.d. processes on the <jats:italic>d<\/jats:italic>-regular tree for <jats:italic>d<\/jats:italic> \u2265 3. We show that if such a process is restricted to two distant connected subgraphs of the tree, then the two parts are basically uncorrelated. More precisely, any functions of the two parts have correlation at most <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0963548317000360_inline1\" \/><jats:tex-math>$k(d-1) \/ (\\sqrt{d-1})^k$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, where <jats:italic>k<\/jats:italic> denotes the distance between the subgraphs. This result can be considered as a quantitative version of the fact that factor of i.i.d. processes have trivial 1-ended tails.<\/jats:p>","DOI":"10.1017\/s0963548317000360","type":"journal-article","created":{"date-parts":[[2017,8,1]],"date-time":"2017-08-01T02:14:26Z","timestamp":1501553666000},"page":"1-20","source":"Crossref","is-referenced-by-count":2,"title":["Correlation Bounds for Distant Parts of Factor of IID Processes"],"prefix":"10.1017","volume":"27","author":[{"given":"\u00c1GNES","family":"BACKHAUSZ","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"BAL\u00c1ZS","family":"GERENCS\u00c9R","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"VIKTOR","family":"HARANGI","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M\u00c1T\u00c9","family":"VIZER","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2017,8,1]]},"reference":[{"key":"S0963548317000360_ref13","doi-asserted-by":"publisher","DOI":"10.4171\/GGD\/395"},{"key":"S0963548317000360_ref22","doi-asserted-by":"publisher","DOI":"10.1353\/ajm.2013.0024"},{"key":"S0963548317000360_ref26","doi-asserted-by":"publisher","DOI":"10.1007\/BF02790325"},{"key":"S0963548317000360_ref21","doi-asserted-by":"publisher","DOI":"10.4236\/ojdm.2016.64018"},{"key":"S0963548317000360_ref18","doi-asserted-by":"publisher","DOI":"10.1214\/14-AOP952"},{"key":"S0963548317000360_ref15","volume-title":"A Proof of Alon's Second Eigenvalue Conjecture and Related Problems","author":"Friedman","year":"2008"},{"key":"S0963548317000360_ref11","doi-asserted-by":"publisher","DOI":"10.1017\/fms.2016.14"},{"key":"S0963548317000360_ref19","doi-asserted-by":"crossref","unstructured":"Hoppen C. and Wormald N. 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