{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,8]],"date-time":"2025-05-08T12:43:05Z","timestamp":1746708185581},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2020,11,5]],"date-time":"2020-11-05T00:00:00Z","timestamp":1604534400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2021,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove two estimates for the expectation of the exponential of a complex function of a random permutation or subset. Using this theory, we find asymptotic expressions for the expected number of copies and induced copies of a given graph in a uniformly random graph with degree sequence(<jats:italic>d<\/jats:italic><jats:sub><jats:italic>1<\/jats:italic><\/jats:sub>, \u2026, <jats:italic>d<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>) as <jats:italic>n<\/jats:italic>\u2192 \u221e. We also determine the expected number of spanning trees in this model. The range of degrees covered includes <jats:italic>d<\/jats:italic><jats:sub><jats:italic>j<\/jats:italic><\/jats:sub>= \u03bb<jats:italic>n<\/jats:italic> + <jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic><jats:sup>1\/2+<jats:italic>\u03b5<\/jats:italic><\/jats:sup>) for some \u03bb bounded away from 0 and 1.<\/jats:p>","DOI":"10.1017\/s0963548320000498","type":"journal-article","created":{"date-parts":[[2020,11,5]],"date-time":"2020-11-05T06:39:37Z","timestamp":1604558377000},"page":"460-497","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":1,"title":["Subgraph counts for dense random graphs with specified degrees"],"prefix":"10.1017","volume":"30","author":[{"given":"Catherine","family":"Greenhill","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mikhail","family":"Isaev","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Brendan D.","family":"McKay","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2020,11,5]]},"reference":[{"key":"S0963548320000498_ref10","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1016\/S0195-6698(13)80042-X","article-title":"Asymptotic enumeration by degree sequence of graphs of high degree","volume":"11","author":"McKay","year":"1990","journal-title":"European J. Combin."},{"key":"S0963548320000498_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2017.02.003"},{"key":"S0963548320000498_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/s11424-008-9141-7"},{"key":"S0963548320000498_ref2","first-page":"264","article-title":"Graphs with prescribed degrees of vertices (Hungarian)","volume":"11","author":"Erd\u0151s","year":"1960","journal-title":"Mat. Lapok"},{"key":"S0963548320000498_ref11","unstructured":"[11] Moon, J. W. (1970) Counting Labelled Trees, Vol. 1 of Canadian Mathematical Monographs. Canadian Mathematical Congress."},{"key":"S0963548320000498_ref7","doi-asserted-by":"crossref","unstructured":"[7] McDiarmid, C. (1998) Concentration. In Probabilistic Methods for Algorithmic Discrete Mathematics, Vol. 16 of Algorithms and Combinatorics, pp. 195\u2013248. Springer.","DOI":"10.1007\/978-3-662-12788-9_6"},{"key":"S0963548320000498_ref8","first-page":"15","article-title":"Asymptotics for symmetric 0\u20131 matrices with prescribed row sums","volume":"19A","author":"McKay","year":"1985","journal-title":"Ars Combin."},{"key":"S0963548320000498_ref6","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.1013"},{"key":"S0963548320000498_ref4","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1002\/rsa.20754","article-title":"Complex martingales and asymptotic enumeration","volume":"52","author":"Isaev","year":"2018","journal-title":"Random Struct. Algorithms"},{"key":"S0963548320000498_ref9","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1017\/S0963548311000034","article-title":"Subgraphs of dense random graphs with specified degrees","volume":"20","author":"McKay","year":"2011","journal-title":"Combin. Probab. Comput."},{"key":"S0963548320000498_ref5","doi-asserted-by":"crossref","first-page":"1961","DOI":"10.1016\/j.disc.2006.09.032","article-title":"Small subgraphs of random regular graphs","volume":"307","author":"Kim","year":"2007","journal-title":"Discrete Math."},{"key":"S0963548320000498_ref1","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/s00245-003-0776-4","article-title":"Conditional essential suprema with applications","volume":"48","author":"Barron","year":"2003","journal-title":"Appl. Math. Optim."}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548320000498","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,13]],"date-time":"2021-04-13T11:58:54Z","timestamp":1618315134000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548320000498\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,5]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,5]]}},"alternative-id":["S0963548320000498"],"URL":"https:\/\/doi.org\/10.1017\/s0963548320000498","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,5]]},"assertion":[{"value":"\u00a9 The Author(s), 2020. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}