{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,22]],"date-time":"2024-03-22T13:08:48Z","timestamp":1711112928486},"reference-count":11,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2002,5,31]],"date-time":"2002-05-31T00:00:00Z","timestamp":1022803200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[2002,7]]},"abstract":"Abstract<\/jats:title>In this paper we study the covariance structure of the number of nodes k<\/jats:italic> and l<\/jats:italic> steps away from the root in random recursive trees. We give an analytic expression valid for all k, l<\/jats:italic> and tree sizes N.<\/jats:italic> The fraction of nodes k<\/jats:italic> steps away from the root is a random probability distribution in k.<\/jats:italic> The expression for the covariances allows us to show that the total variation distance between this (random) probability distribution and its mean converges in probability to zero. \u00a9 2002 Wiley Periodicals, Inc. Random Struct. Alg., 20: 519\u2013539, 2002<\/jats:p>","DOI":"10.1002\/rsa.10030","type":"journal-article","created":{"date-parts":[[2002,10,6]],"date-time":"2002-10-06T12:27:22Z","timestamp":1033907242000},"page":"519-539","source":"Crossref","is-referenced-by-count":22,"title":["On the covariance of the level sizes in random recursive trees"],"prefix":"10.1002","volume":"20","author":[{"given":"Remco","family":"van der Hofstad","sequence":"first","affiliation":[]},{"given":"Gerard","family":"Hooghiemstra","sequence":"additional","affiliation":[]},{"given":"Piet","family":"Van Mieghem","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2002,5,31]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Handbook of mathematical functions","author":"Abramowitz M.","year":"1968"},{"key":"e_1_2_1_3_2","volume-title":"Random graphs","author":"Bollob\u00e1s B.","year":"1985"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1098-2418(199608\/09)9:1\/2<79::AID-RSA5>3.0.CO;2-8"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1017\/S026996480115206X"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1978-085-0"},{"key":"e_1_2_1_7_2","series-title":"London Mathematical Society Lecture Notes Series","first-page":"125","volume-title":"The distance between nodes in recursive trees","author":"Moon J. W.","year":"1974"},{"key":"e_1_2_1_8_2","first-page":"1","article-title":"A survey of recursive trees","volume":"51","author":"Smythe R. T.","year":"1995","journal-title":"Theor Prob Math Stat"},{"key":"e_1_2_1_9_2","first-page":"313","volume-title":"On the maximum degree and the height of a random recursive tree","author":"Szyma\u0144ski J.","year":"1990"},{"key":"e_1_2_1_10_2","volume-title":"Combinatorical identities","author":"Riordan J.","year":"1968"},{"key":"e_1_2_1_11_2","volume-title":"Introduction to the theory of Fourier integrals","author":"Titchmarsh E. C.","year":"1949"},{"key":"e_1_2_1_12_2","unstructured":"P.Van Mieghem G.Hooghiemstra andR.van der Hofstad A scaling law for the hopcount Delft Report 2000125 Delft University Delft The Netherlands http:\/\/wwwtvs.et.tudelft.nl\/people\/piet\/telconference.html."}],"container-title":["Random Structures & Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Frsa.10030","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rsa.10030","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,18]],"date-time":"2023-11-18T13:13:32Z","timestamp":1700313212000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/rsa.10030"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,5,31]]},"references-count":11,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2002,7]]}},"alternative-id":["10.1002\/rsa.10030"],"URL":"https:\/\/doi.org\/10.1002\/rsa.10030","archive":["Portico"],"relation":{},"ISSN":["1042-9832","1098-2418"],"issn-type":[{"value":"1042-9832","type":"print"},{"value":"1098-2418","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,5,31]]}}}