{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T19:59:28Z","timestamp":1769975968939,"version":"3.49.0"},"reference-count":20,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2019,10,24]],"date-time":"2019-10-24T00:00:00Z","timestamp":1571875200000},"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":[[2020,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The Brownian separable permuton is a random probability measure on the unit square, which was introduced by Bassino, Bouvel, F\u00e9ray, Gerin and Pierrot (2016) as the scaling limit of the diagram of the uniform separable permutation as size grows to infinity. We show that, almost surely, the permuton is the pushforward of the Lebesgue measure on the graph of a random measure-preserving function associated to a Brownian excursion whose strict local minima are decorated with independent and identically distributed signs. As a consequence, its support is almost surely totally disconnected, has Hausdorff dimension one, and enjoys self-similarity properties inherited from those of the Brownian excursion. The density function of the averaged permuton is computed and a connection with the shuffling of the Brownian continuum random tree is explored.<\/jats:p>","DOI":"10.1017\/s0963548319000300","type":"journal-article","created":{"date-parts":[[2019,10,24]],"date-time":"2019-10-24T13:03:35Z","timestamp":1571922215000},"page":"241-266","source":"Crossref","is-referenced-by-count":12,"title":["On the Brownian separable permuton"],"prefix":"10.1017","volume":"29","author":[{"given":"Micka\u00ebl","family":"Maazoun","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2019,10,24]]},"reference":[{"key":"S0963548319000300_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2012.09.003"},{"key":"S0963548319000300_ref14","unstructured":"[14] Ghys, E. (2017) A Singular Mathematical Promenade, ENS \u00c9ditions."},{"key":"S0963548319000300_ref4","first-page":"129","article-title":"On pop-stacks in series","volume":"19","author":"Avis","year":"1981","journal-title":"Utilitas Math"},{"key":"S0963548319000300_ref2","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176989404"},{"key":"S0963548319000300_ref1","doi-asserted-by":"publisher","DOI":"10.1214\/ECP.v20-4250"},{"key":"S0963548319000300_ref3","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176988720"},{"key":"S0963548319000300_ref17","doi-asserted-by":"publisher","DOI":"10.1214\/154957805100000140"},{"key":"S0963548319000300_ref5","doi-asserted-by":"publisher","DOI":"10.1214\/17-AOP1223"},{"key":"S0963548319000300_ref16","doi-asserted-by":"crossref","unstructured":"[16] Kingman, J. F. C. (1993) Poisson Processes, Vol. 3 of Oxford Studies in Probability, Oxford University Press.","DOI":"10.1093\/oso\/9780198536932.001.0001"},{"key":"S0963548319000300_ref18","unstructured":"[18] Ouchterlony, E. (2005) On young tableau involutions and patterns in permutations. Link\u00f6ping Studies in Science and Technology. Dissertations No. 993, Link\u00f6pings universitet, Sweden."},{"key":"S0963548319000300_ref6","doi-asserted-by":"crossref","unstructured":"[6] Bassino, F. , Bouvel, M. , F\u00e9ray, V. , Gerin, L. , Maazoun, M. and Pierrot, A. (2019) Universal limits of substitution-closed permutation classes. J. Eur. Math. Soc.","DOI":"10.4171\/JEMS\/993"},{"key":"S0963548319000300_ref13","unstructured":"[13] Duquesne, T. (2006) The coding of compact real trees by real valued functions. arXiv:math\/0604106"},{"key":"S0963548319000300_ref8","first-page":"147","article-title":"Path transformations connecting Brownian bridge, excursion and meander","volume":"118","author":"Bertoin","year":"1994","journal-title":"Bull. Sci. Math"},{"key":"S0963548319000300_ref9","doi-asserted-by":"publisher","DOI":"10.1201\/9780203494370"},{"key":"S0963548319000300_ref19","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2014.04.008"},{"key":"S0963548319000300_ref12","first-page":"1","article-title":"The expected shape of random doubly alternating Baxter permutations","volume":"9","author":"Dokos","year":"2014","journal-title":"Online J. Anal. Combin"},{"key":"S0963548319000300_ref20","doi-asserted-by":"publisher","DOI":"10.1137\/0404025"},{"key":"S0963548319000300_ref11","first-page":"200","volume-title":"Algorithms and Data Structures: Third Workshop: WADS \u201993","author":"Bose","year":"1993"},{"key":"S0963548319000300_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8163-0"},{"key":"S0963548319000300_ref7","unstructured":"[7] Bassino, F. , Bouvel, M. , F\u00e9ray, V. , Gerin, L. , Maazoun, M. and Pierrot, A. (2019) Scaling limits of permutation classes with a finite specification: A dichotomy. arXiv:1903.07522"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548319000300","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,25]],"date-time":"2024-07-25T15:37:41Z","timestamp":1721921861000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548319000300\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,24]]},"references-count":20,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["S0963548319000300"],"URL":"https:\/\/doi.org\/10.1017\/s0963548319000300","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,24]]}}}