{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T06:44:48Z","timestamp":1760597088094},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2001,6,25]],"date-time":"2001-06-25T00:00:00Z","timestamp":993427200000},"content-version":"unspecified","delay-in-days":55,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2001,5]]},"abstract":"<jats:p>Let (<jats:italic>X<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>) be a residual allocation model with i.i.d. residual fractions \n<jats:italic>U<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>: For <jats:italic>W<\/jats:italic> a random \nvariable with values in [0; 1] and independent of (<jats:italic>X<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>), \nwe define another sequence (<jats:italic>Y<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>) by setting<\/jats:p><jats:p>(formula here)<\/jats:p><jats:p>Under minor regularity assumptions we show that (<jats:italic>X<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>) and (<jats:italic>Y<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>) \nhave the same probability law if and only if this law is a GEM distribution. In this case, the distribution of <jats:italic>W<\/jats:italic> \nand the <jats:italic>U<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>s is Beta(1; \u03b8) for some \u03b8 &gt; 0.<\/jats:p>","DOI":"10.1017\/s0963548301004692","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T09:16:52Z","timestamp":1027761412000},"page":"213-217","source":"Crossref","is-referenced-by-count":10,"title":["A Characterization of GEM Distributions"],"prefix":"10.1017","volume":"10","author":[{"given":"ALEXANDER","family":"GNEDIN","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"SERGEI","family":"KEROV","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2001,6,25]]},"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548301004692","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,31]],"date-time":"2019-03-31T15:06:27Z","timestamp":1554044787000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548301004692\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,5]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2001,5]]}},"alternative-id":["S0963548301004692"],"URL":"https:\/\/doi.org\/10.1017\/s0963548301004692","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,5]]}}}