{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T16:15:10Z","timestamp":1775060110843,"version":"3.50.1"},"reference-count":29,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2012,7,3]],"date-time":"2012-07-03T00:00:00Z","timestamp":1341273600000},"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":[[2012,9]]},"abstract":"<jats:p>We consider random permutations derived by sampling from stick-breaking partitions of the unit interval. The cycle structure of such a permutation can be associated with the path of a decreasing Markov chain on<jats:italic>n<\/jats:italic>integers. Under certain assumptions on the stick-breaking factor we prove a central limit theorem for the logarithm of the order of the permutation, thus extending the classical Erd\u0151s\u2013Tur\u00e1n law for the uniform permutations and its generalization for Ewens' permutations associated with sampling from the PD\/GEM(\u03b8)-distribution. Our approach is based on using perturbed random walks to obtain the limit laws for the sum of logarithms of the cycle lengths.<\/jats:p>","DOI":"10.1017\/s0963548312000247","type":"journal-article","created":{"date-parts":[[2012,7,3]],"date-time":"2012-07-03T11:53:51Z","timestamp":1341316431000},"page":"715-733","source":"Crossref","is-referenced-by-count":9,"title":["A Generalization of the Erd\u0151s\u2013Tur\u00e1n Law for the Order of Random Permutation"],"prefix":"10.1017","volume":"21","author":[{"given":"ALEXANDER","family":"GNEDIN","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ALEXANDER","family":"IKSANOV","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ALEXANDER","family":"MARYNYCH","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2012,7,3]]},"reference":[{"key":"S0963548312000247_ref11","doi-asserted-by":"publisher","DOI":"10.3150\/bj\/1077544604"},{"key":"S0963548312000247_ref28","unstructured":"[28] Negadailov P. (2010) Limit theorems for random recurrences and renewal-type processes. PhD thesis, Utrecht University."},{"key":"S0963548312000247_ref14","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139107174.013"},{"key":"S0963548312000247_ref1","volume-title":"Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables","author":"Abramowitz","year":"1964"},{"key":"S0963548312000247_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/BF00534892"},{"key":"S0963548312000247_ref5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022419328971"},{"key":"S0963548312000247_ref8","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1985.119.287"},{"key":"S0963548312000247_ref25","first-page":"273","article-title":"An analytic method in probabilistic combinatorics","volume":"46","author":"Manstavi\u010dius","year":"2009","journal-title":"Osaka J. Math."},{"key":"S0963548312000247_ref24","doi-asserted-by":"publisher","DOI":"10.1109\/18.761251"},{"key":"S0963548312000247_ref16","doi-asserted-by":"crossref","unstructured":"[16] Gnedin A. , Iksanov A. and Marynych A. (2010) The Bernoulli sieve: an overview. Discr. Math. Theoret. Comput. Sci. Proceedings Series, AM, 329\u2013342.","DOI":"10.46298\/dmtcs.2770"},{"key":"S0963548312000247_ref27","first-page":"46","article-title":"Randomized decomposable statistics in a generalized allocation scheme over a countable set of cells","volume":"1","author":"Mirakhmedov","year":"1989","journal-title":"Diskretnaya Matematika"},{"key":"S0963548312000247_ref23","volume-title":"Characteristic Functions","author":"Lukacs","year":"1970"},{"key":"S0963548312000247_ref18","doi-asserted-by":"crossref","unstructured":"[18] Gnedin A. , Iksanov A. and Roesler U. (2008) Small parts in the Bernoulli sieve. Discr. Math. Theoret. Comput. Sci. Proceedings Series, AI, 239\u2013246.","DOI":"10.46298\/dmtcs.3567"},{"key":"S0963548312000247_ref17","doi-asserted-by":"publisher","DOI":"10.1214\/08-AAP592"},{"key":"S0963548312000247_ref4","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.3240030310"},{"key":"S0963548312000247_ref29","volume-title":"Combinatorial Stochastic Processes","author":"Pitman","year":"2006"},{"key":"S0963548312000247_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02280290"},{"key":"S0963548312000247_ref20","doi-asserted-by":"publisher","DOI":"10.1214\/009117904000000801"},{"key":"S0963548312000247_ref6","doi-asserted-by":"publisher","DOI":"10.1214\/10-AAP697"},{"key":"S0963548312000247_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2010.09.027"},{"key":"S0963548312000247_ref3","doi-asserted-by":"publisher","DOI":"10.4171\/000"},{"key":"S0963548312000247_ref19","doi-asserted-by":"crossref","unstructured":"[19] Gnedin A. and Olshanski G. (2006) Coherent permutations with descent statistic and the boundary problem for the graph of zigzag diagrams. Intern. Math. Res. Not. # 51968.","DOI":"10.1155\/IMRN\/2006\/51968"},{"key":"S0963548312000247_ref12","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548303005996"},{"key":"S0963548312000247_ref2","volume-title":"Introduction to Analytic Number Theory","author":"Apostol","year":"1976"},{"key":"S0963548312000247_ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2012.04.010"},{"key":"S0963548312000247_ref15","first-page":"44","article-title":"Limit theorems for the number of occupied boxes in the Bernoulli sieve","volume":"16","author":"Gnedin","year":"2010","journal-title":"Theory of Stochastic Processes"},{"key":"S0963548312000247_ref21","unstructured":"[21] Iksanov A. On the number of empty boxes in the Bernoulli sieve I. Stochastics, to appear."},{"key":"S0963548312000247_ref9","volume-title":"IMS Lecture Notes, Monograph Series","author":"Diaconis","year":"1988"},{"key":"S0963548312000247_ref26","doi-asserted-by":"publisher","DOI":"10.1137\/1122075"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548312000247","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,20]],"date-time":"2022-01-20T03:13:33Z","timestamp":1642648413000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548312000247\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,7,3]]},"references-count":29,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2012,9]]}},"alternative-id":["S0963548312000247"],"URL":"https:\/\/doi.org\/10.1017\/s0963548312000247","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,7,3]]}}}