{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T20:04:24Z","timestamp":1695845064174},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2022,4,29]],"date-time":"2022-04-29T00:00:00Z","timestamp":1651190400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2022,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For a uniform random labelled tree, we find the limiting distribution of tree parameters which are stable (in some sense) with respect to local perturbations of the tree structure. The proof is based on the martingale central limit theorem and the Aldous\u2013Broder algorithm. In particular, our general result implies the asymptotic normality of the number of occurrences of any given small pattern and the asymptotic log-normality of the number of automorphisms.<\/jats:p>","DOI":"10.1017\/s0963548321000523","type":"journal-article","created":{"date-parts":[[2022,4,29]],"date-time":"2022-04-29T12:13:38Z","timestamp":1651234418000},"page":"737-764","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":1,"title":["Distribution of tree parameters by martingale approach"],"prefix":"10.1017","volume":"31","author":[{"given":"Mikhail","family":"Isaev","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Angus","family":"Southwell","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maksim","family":"Zhukovskii","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2022,4,29]]},"reference":[{"key":"S0963548321000523_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/S0021900200008706"},{"key":"S0963548321000523_ref21","volume-title":"Canadian Mathematical Monographs","volume":"1","author":"Moon","year":"1970"},{"key":"S0963548321000523_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(77)90045-4"},{"key":"S0963548321000523_ref22","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548304006133"},{"key":"S0963548321000523_ref6","author":"Cooper","year":"2009"},{"key":"S0963548321000523_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548307008425"},{"key":"S0963548321000523_ref15","unstructured":"[15] Isaev, M. , Southwell, A. and Zhukovskii, M. Distribution of tree parameters by martingale approach, e-preprint arXiv:1912.09838."},{"key":"S0963548321000523_ref28","unstructured":"[28] Wagner, S. and Stufler, B. (2016) The number of automorphisms of random trees, a talk at BIRS Workshop, October 2016."},{"key":"S0963548321000523_ref18","first-page":"53","article-title":"P\u00f3lya urn models and connections to random trees: a review","volume":"2","author":"Mahmoud","year":"2004","journal-title":"J. Iranian Stat. 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Zametki"},{"key":"S0963548321000523_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(96)00094-4"},{"key":"S0963548321000523_ref4","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177693494"},{"key":"S0963548321000523_ref30","unstructured":"[30] Yu, L. (2012) Automorphisms of random trees, PhD Thesis, Drexel University."},{"key":"S0963548321000523_ref29","unstructured":"[29] Wagner, S. (2019) personal communication."},{"key":"S0963548321000523_ref27","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548314000443"},{"key":"S0963548321000523_ref23","doi-asserted-by":"publisher","DOI":"10.3150\/12-BEJ417"},{"key":"S0963548321000523_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/S0021900200006100"},{"key":"S0963548321000523_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2017.02.003"},{"key":"S0963548321000523_ref26","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20674"},{"key":"S0963548321000523_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-211-75357-6"},{"key":"S0963548321000523_ref20","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(94)00164-9"},{"key":"S0963548321000523_ref11","unstructured":"[11] Greenhill, C. , Isaev, M. and McKay, B. D. (2018) Subgraph counts for dense random graphs with specified degrees. 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