{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,13]],"date-time":"2023-03-13T16:10:51Z","timestamp":1678723851904},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T00:00:00Z","timestamp":1555459200000},"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":[[2019,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider the asymptotics of the difference between the empirical measures of the <jats:italic>\u03b2<\/jats:italic>-Hermite tridiagonal matrix and its minor. We prove that this difference has a deterministic limit and Gaussian fluctuations. Through a correspondence between measures and continual Young diagrams, this deterministic limit is identified with the Vershik\u2013Kerov\u2013Logan\u2013Shepp curve. Moreover, the Gaussian fluctuations are identified with a sectional derivative of the Gaussian free field.<\/jats:p>","DOI":"10.1017\/s0963548319000087","type":"journal-article","created":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T04:02:46Z","timestamp":1555473766000},"page":"657-674","source":"Crossref","is-referenced-by-count":1,"title":["Discrete derivative asymptotics of the <i>\u03b2<\/i>-Hermite eigenvalues"],"prefix":"10.1017","volume":"28","author":[{"given":"Gopal","family":"Goel","sequence":"first","affiliation":[]},{"given":"Andrew","family":"Ahn","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2019,4,17]]},"reference":[{"key":"S0963548319000087_ref10","first-page":"364","article-title":"Fluctuations of interlacing sequences","volume":"13","author":"Sodin","year":"2017","journal-title":"J. Math. Phys. Anal. Geom."},{"key":"S0963548319000087_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s00440-017-0823-8"},{"key":"S0963548319000087_ref8","doi-asserted-by":"publisher","DOI":"10.1214\/16-ECP38"},{"key":"S0963548319000087_ref5","doi-asserted-by":"publisher","DOI":"10.1063\/1.1507823"},{"key":"S0963548319000087_ref3","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.21546"},{"key":"S0963548319000087_ref7","first-page":"783","article-title":"The random matrix technique of ghosts and shadows","volume":"16","author":"Edelman","year":"2010","journal-title":"Markov Processes and Related Fields."},{"key":"S0963548319000087_ref11","first-page":"527","article-title":"Asymptotics of the Plancherel measure of the symmetric group and the limiting form of Young tableaux","volume":"18","author":"Vershik","year":"1977","journal-title":"Soviet Math. Doklady"},{"key":"S0963548319000087_ref6","doi-asserted-by":"publisher","DOI":"10.1142\/S201032631850003X"},{"key":"S0963548319000087_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511801334"},{"key":"S0963548319000087_ref2","doi-asserted-by":"publisher","DOI":"10.17323\/1609-4514-2014-14-1-29-38"},{"key":"S0963548319000087_ref4","unstructured":"[4] Bufetov, A. (2013) Kerov\u2019s interlacing sequences and random matrices. J. Math. Phys. 54 113302."}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548319000087","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,11]],"date-time":"2019-09-11T07:51:10Z","timestamp":1568188270000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548319000087\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,17]]},"references-count":11,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["S0963548319000087"],"URL":"https:\/\/doi.org\/10.1017\/s0963548319000087","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,4,17]]}}}