{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,8]],"date-time":"2025-05-08T12:42:45Z","timestamp":1746708165666,"version":"3.38.0"},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"A","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2014,12]]},"abstract":"<jats:p>The probability <jats:italic>h<\/jats:italic>(<jats:italic>n<\/jats:italic>, <jats:italic>m<\/jats:italic>) that the block counting process of the Bolthausen-Sznitman <jats:italic>n<\/jats:italic>-coalescent ever visits the state <jats:italic>m<\/jats:italic> is analyzed. It is shown that the asymptotic hitting probabilities <jats:italic>h<\/jats:italic>(<jats:italic>m<\/jats:italic>) = lim<jats:sub>\n                  <jats:italic>n<\/jats:italic>\u2192\u221e<\/jats:sub>\n               <jats:italic>h<\/jats:italic>(<jats:italic>n<\/jats:italic>, <jats:italic>m<\/jats:italic>), <jats:italic>m<\/jats:italic> \u2208 <jats:bold>N<\/jats:bold>, exist and an integral formula for <jats:italic>h<\/jats:italic>(<jats:italic>m<\/jats:italic>) is provided. The proof is based on generating functions and exploits a certain convolution property of the Bolthausen-Sznitman coalescent. It follows that <jats:italic>h<\/jats:italic>(<jats:italic>m<\/jats:italic>) \u223c 1\/log <jats:italic>m<\/jats:italic> as <jats:italic>m<\/jats:italic> \u2192 \u221e. An application to linear recursions is indicated.<\/jats:p>","DOI":"10.1017\/s0021900200021215","type":"journal-article","created":{"date-parts":[[2016,3,30]],"date-time":"2016-03-30T16:25:31Z","timestamp":1459355131000},"page":"87-97","source":"Crossref","is-referenced-by-count":1,"title":["Asymptotic hitting probabilities for the Bolthausen-Sznitman coalescent"],"prefix":"10.1017","volume":"51","author":[{"given":"Martin","family":"M\u00f6hle","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,3,30]]},"reference":[{"key":"S0021900200021215_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700006698"},{"key":"S0021900200021215_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2007.01.011"},{"key":"S0021900200021215_ref7","doi-asserted-by":"publisher","DOI":"10.3150\/bj\/1077544604"},{"volume-title":"Analytic Combinatorics","year":"2009","key":"S0021900200021215_ref6"},{"key":"S0021900200021215_ref5","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20233"},{"key":"S0021900200021215_ref16","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1032374759"},{"key":"S0021900200021215_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s002200050450"},{"volume-title":"The Umbral Calculus","year":"1984","key":"S0021900200021215_ref15"},{"volume-title":"Regular Variation","year":"1987","key":"S0021900200021215_ref2"},{"key":"S0021900200021215_ref14","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1022677552"},{"volume":"84","volume-title":"Graduate Studies Math.","year":"2007","key":"S0021900200021215_ref1"},{"key":"S0021900200021215_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-7915-6_29"},{"volume-title":"Markov Chains","year":"1997","key":"S0021900200021215_ref12"},{"key":"S0021900200021215_ref11","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1127322016"},{"key":"S0021900200021215_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(74)90013-3"},{"key":"S0021900200021215_ref8","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1324046023"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200021215","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,4,22]],"date-time":"2017-04-22T04:44:25Z","timestamp":1492836265000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200021215\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12]]},"references-count":16,"journal-issue":{"issue":"A","published-print":{"date-parts":[[2014,12]]}},"alternative-id":["S0021900200021215"],"URL":"https:\/\/doi.org\/10.1017\/s0021900200021215","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"type":"print","value":"0021-9002"},{"type":"electronic","value":"1475-6072"}],"subject":[],"published":{"date-parts":[[2014,12]]}}}